A025322 -id:A025322

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Search: a025322 -id:a025322

Displaying 1-10 of 18 results found.

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A024796

Numbers expressible in more than one way as i^2 + j^2 + k^2, where 1 <= i <= j <= k.

+10
24

27, 33, 38, 41, 51, 54, 57, 59, 62, 66, 69, 74, 75, 77, 81, 83, 86, 89, 90, 94, 98, 99, 101, 102, 105, 107, 108, 110, 113, 114, 117, 118, 121, 122, 123, 125, 126, 129, 131, 132, 134, 137, 138, 139, 141, 146, 147, 149, 150, 152, 153, 154, 155, 158, 161, 162, 164, 165, 166, 170 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	COMMENTS	`a(n) multiplied by (h^2)/(8ma^2) is the n-th energy level exhibiting accidental degeneracy, for a quantum mechanical particle of mass m in a cubic box of side length a (h is Planck's constant). - A. Timothy Royappa, Feb 12 2019`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..8057`
	FORMULA	`{n: A025427(n) > 1 }. - R. J. Mathar, Aug 05 2022`
	MATHEMATICA	`okQ[n_]:= Length[Select[PowersRepresentations[n, 3, 2], !MemberQ[#, 0] &]] > 1; (* Jinyuan Wang, Feb 12 2019 *)`
	CROSSREFS	`Cf. A000408, A007692, A008917, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025367, A025427.`
	KEYWORD	`nonn`
	AUTHOR	`Clark Kimberling`
	STATUS	`approved`

A025333

Numbers that are the sum of 3 nonzero squares in 5 or more ways.

+10
22

194, 206, 209, 230, 266, 269, 281, 297, 306, 314, 321, 326, 329, 341, 342, 350, 354, 369, 374, 381, 386, 389, 398, 401, 402, 413, 414, 419, 425, 426, 434, 437, 441, 446, 449, 450, 458, 459, 461, 470, 474, 482, 486, 489, 491, 494, 497, 506, 509, 513, 521, 525, 530, 531 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..6628` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025296, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025370, A025427, A343967.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025332

Numbers that are the sum of 3 nonzero squares in 4 or more ways.

+10
21

129, 134, 146, 153, 161, 171, 189, 194, 198, 201, 206, 209, 230, 234, 243, 246, 249, 251, 254, 257, 261, 266, 269, 270, 278, 281, 285, 290, 293, 294, 297, 299, 306, 314, 321, 326, 329, 339, 341, 342, 350, 353, 354, 362, 363, 365, 369, 371, 374, 378, 381, 386, 387, 389 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..7221` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025295, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025369, A025427, A343968.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025334

Numbers that are the sum of 3 nonzero squares in 6 or more ways.

+10
21

209, 297, 306, 314, 321, 326, 329, 341, 342, 369, 374, 425, 426, 434, 441, 446, 458, 459, 461, 486, 489, 494, 497, 506, 509, 513, 521, 530, 531, 534, 542, 545, 546, 549, 558, 561, 566, 569, 581, 593, 594, 602, 605, 614, 621, 626, 629, 633, 641, 649, 650, 654, 657, 659 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..6187` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025297, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025371, A025427, A345083.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025335

Numbers that are the sum of 3 nonzero squares in 7 or more ways.

+10
21

341, 369, 374, 446, 461, 486, 494, 506, 509, 521, 545, 549, 566, 569, 581, 594, 614, 621, 626, 629, 641, 654, 666, 677, 686, 689, 701, 710, 726, 729, 731, 734, 749, 761, 770, 774, 789, 794, 797, 801, 806, 809, 810, 818, 821, 825, 833, 846, 849, 854, 857, 866, 869, 881 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..5480` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025298, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025372, A025427, A345086.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025336

Numbers that are the sum of 3 nonzero squares in 8 or more ways.

+10
21

374, 446, 486, 521, 566, 569, 594, 614, 621, 626, 629, 686, 689, 701, 710, 729, 734, 749, 761, 770, 774, 789, 794, 801, 809, 810, 825, 846, 849, 854, 857, 866, 869, 881, 902, 909, 914, 926, 929, 941, 945, 950, 953, 965, 969, 971, 974, 986, 989, 990, 1001, 1014, 1022 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..5058` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025299, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025373, A025427, A345087.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025337

Numbers that are the sum of 3 nonzero squares in 9 or more ways.

+10
21

594, 614, 626, 689, 734, 761, 774, 794, 801, 846, 854, 866, 881, 909, 914, 926, 929, 941, 950, 965, 974, 986, 989, 990, 1001, 1025, 1026, 1034, 1041, 1046, 1049, 1062, 1070, 1074, 1089, 1091, 1097, 1106, 1109, 1118, 1121, 1130, 1134, 1139, 1154, 1161, 1166 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..4409` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025300, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025374, A025427, A345119.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025338

Numbers that are the sum of 3 nonzero squares in 10 or more ways.

+10
21

594, 734, 761, 794, 801, 846, 854, 866, 881, 909, 926, 941, 950, 965, 986, 1001, 1026, 1034, 1041, 1046, 1049, 1089, 1106, 1109, 1121, 1130, 1154, 1161, 1169, 1181, 1190, 1206, 1209, 1214, 1226, 1238, 1265, 1274, 1286, 1301, 1314, 1322, 1326, 1329, 1341 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..4009` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025301, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025375, A025427, A345121.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025331

Numbers that are the sum of 3 nonzero squares in 3 or more ways.

+10
20

54, 66, 81, 86, 89, 99, 101, 110, 114, 126, 129, 131, 134, 146, 149, 150, 153, 161, 162, 166, 171, 173, 174, 179, 182, 185, 186, 189, 194, 198, 201, 206, 209, 216, 219, 221, 222, 225, 227, 230, 233, 234, 237, 241, 242, 243, 245, 246, 249, 251, 254, 257, 258, 261, 264 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Robert Price, Table of n, a(n) for n = 1..7639` `Index entries for sequences related to sums of squares`
	CROSSREFS	`Cf. A024796, A025294, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338, A025368, A025398, A025427.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

A025323

Numbers that are the sum of 3 nonzero squares in exactly 3 ways.

+10
19

54, 66, 81, 86, 89, 99, 101, 110, 114, 126, 131, 149, 150, 162, 166, 173, 174, 179, 182, 185, 186, 216, 219, 221, 222, 225, 227, 233, 237, 241, 242, 245, 258, 264, 274, 275, 286, 291, 302, 305, 309, 315, 318, 323, 324, 334, 338, 344, 347, 349, 356, 361, 366, 377, 396 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`David A. Corneth, Table of n, a(n) for n = 1..1069 (first 418 terms from Robert Price, terms < 210^6)` `David A. Corneth, PARI program` `David A. Corneth, Terms below (inclusive) 210^6 with the sums of squares` `Eric Weisstein's World of Mathematics, Square Number.` `Index entries for sequences related to sums of squares`
	FORMULA	`{n: A025427(n) = 3}. - R. J. Mathar, Aug 05 2022`
	EXAMPLE	`182 is a term because 182 = 1^2 + 9^2 + 10^2 = 2^2 + 3^2 + 13^2 = 5^2 + 6^2 + 11^2 and there are no more such sums of three nonzero squares giving 182. - David A. Corneth, Feb 13 2019`
	MATHEMATICA	`Select[Range@ 400, Length@ # == 3 &@ DeleteCases[PowersRepresentations[#, 3, 2], _?(AnyTrue[#, # == 0 &] &)] &] (* Michael De Vlieger, Feb 13 2019 *)`
	PROG	`(PARI) See Corneth link \\ David A. Corneth, Feb 13 2019`
	CROSSREFS	`Cf. A024796, A025427, A025322, A025323, A025324, A025325, A025326, A025327, A025328, A025329, A025330, A025331, A025332, A025333, A025334, A025335, A025336, A025337, A025338.`
	KEYWORD	`nonn`
	AUTHOR	`David W. Wilson`
	STATUS	`approved`

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Last modified July 19 22:34 EDT 2024. Contains 374441 sequences. (Running on oeis4.)