A345146 -id:A345146 - cp's OEIS frontend

A345152 Numbers that are the sum of four third powers in eight or more ways.

21896, 27720, 30429, 31339, 31402, 33579, 34624, 34776, 36162, 36225, 40105, 42120, 42695, 44037, 44163, 44226, 44947, 45162, 45675, 46277, 46683, 46872, 46900, 47600, 48321, 48825, 49042, 50112, 50689, 50806, 50904, 51058, 51408, 51480, 51506, 51597, 51688

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3  = 1^3 + 16^3 + 17^3 + 26^3  = 2^3 + 12^3 + 21^3 + 25^3  = 3^3 + 3^3 + 14^3 + 29^3  = 4^3 + 17^3 + 21^3 + 23^3  = 5^3 + 11^3 + 15^3 + 28^3  = 6^3 + 6^3 + 22^3 + 25^3  = 7^3 + 14^3 + 18^3 + 26^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025373, A344924, A345087, A345146, A345150, A345153, A345183.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 8])
for x in range(len(rets)):
    print(rets[x])

A345119 Numbers that are the sum of three third powers in nine or more ways.

Original entry on oeis.org

14926248, 16819704, 20168784, 34012224, 44946000, 45580536, 54042624, 58995000, 59768064, 62099136, 66203136, 67956624, 69190848, 69393024, 71319312, 72505152, 78008832, 78716448, 79539832, 80621568, 80996544, 89354448, 90757584, 92853216, 94118760, 95331816

Offset: 1

David Consiglio, Jr., Jun 08 2021

nonn

			14926248 is a term because 14926248 = 2^3 + 33^3 + 245^3  = 11^3 + 185^3 + 203^3  = 14^3 + 32^3 + 245^3  = 50^3 + 113^3 + 236^3  = 71^3 + 89^3 + 239^3  = 74^3 + 189^3 + 196^3  = 89^3 + 185^3 + 197^3  = 98^3 + 148^3 + 219^3  = 105^3 + 149^3 + 217^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..37

Cf. A025337, A344750, A345087, A345120, A345121, A345146.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 9])
for x in range(len(rets)):
    print(rets[x])

A345185 Numbers that are the sum of five third powers in nine or more ways.

Original entry on oeis.org

5860, 6112, 6138, 6462, 6497, 6588, 6651, 6859, 6947, 7001, 7038, 7057, 7064, 7099, 7190, 7316, 7328, 7372, 7433, 7561, 7587, 7703, 7759, 7841, 7902, 8056, 8163, 8289, 8352, 8371, 8443, 8506, 8560, 8569, 8630, 8632, 8758, 8928, 8991, 9017, 9045, 9080, 9099

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			6112 is a term because 6112 = 1^3 + 2^3 + 9^3 + 11^3 + 14^3  = 1^3 + 3^3 + 7^3 + 12^3 + 14^3  = 1^3 + 6^3 + 6^3 + 7^3 + 16^3  = 2^3 + 2^3 + 9^3 + 9^3 + 15^3  = 2^3 + 3^3 + 5^3 + 11^3 + 15^3  = 2^3 + 8^3 + 9^3 + 9^3 + 14^3  = 3^3 + 3^3 + 3^3 + 4^3 + 17^3  = 3^3 + 5^3 + 8^3 + 11^3 + 14^3  = 8^3 + 8^3 + 8^3 + 11^3 + 12^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A341891, A344802, A345146, A345183, A345186, A345187, A345518.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 9])
for x in range(len(rets)):
    print(rets[x])

A344926 Numbers that are the sum of four fourth powers in nine or more ways.

Original entry on oeis.org

328118259, 385202034, 395613234, 489597858, 592417938, 625839858, 641398338, 674511618, 677125218, 693239634, 699598578, 722302434, 779889314, 780278643, 780595299, 781388643, 782999714, 791204514, 792005379, 797405714, 797935698, 803898018, 805299699

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

			328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4  = 8^4 + 79^4 + 93^4 + 121^4  = 18^4 + 79^4 + 97^4 + 119^4  = 21^4 + 77^4 + 98^4 + 119^4  = 27^4 + 77^4 + 94^4 + 121^4  = 34^4 + 77^4 + 89^4 + 123^4  = 46^4 + 57^4 + 103^4 + 119^4  = 49^4 + 77^4 + 77^4 + 126^4  = 61^4 + 66^4 + 77^4 + 127^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..79

Cf. A341891, A344750, A344924, A344927, A344928, A345146.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 9])
for x in range(len(rets)):
    print(rets[x])

A345154 Numbers that are the sum of four third powers in exactly nine ways.

Original entry on oeis.org

42120, 46683, 50806, 50904, 51408, 51480, 51688, 52208, 53865, 54971, 56385, 57113, 60515, 60984, 62433, 65303, 66276, 66339, 66430, 67158, 69048, 69832, 69930, 71162, 72072, 72520, 72576, 72800, 73017, 77714, 77903, 79345, 79667, 79849, 80066, 80073, 81207

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345146 at term 1 because 21896 = 1^3 + 11^3 + 19^3 + 22^3 = 2^3 + 2^3 + 12^3 + 26^3 = 2^3 + 3^3 + 19^3 + 23^3 = 2^3 + 5^3 + 15^3 + 25^3 = 3^3 + 10^3 + 16^3 + 24^3 = 3^3 + 17^3 + 19^3 + 19^3 = 4^3 + 6^3 + 20^3 + 22^3 = 5^3 + 8^3 + 14^3 + 25^3 = 7^3 + 11^3 + 17^3 + 23^3 = 8^3 + 9^3 + 19^3 + 22^3.

			42120 is a term because 42120 = 1^3 + 19^3 + 22^3 + 27^3  = 2^3 + 3^3 + 13^3 + 33^3  = 2^3 + 6^3 + 17^3 + 32^3  = 3^3 + 3^3 + 20^3 + 31^3  = 3^3 + 17^3 + 20^3 + 29^3  = 3^3 + 13^3 + 14^3 + 32^3  = 6^3 + 15^3 + 16^3 + 31^3  = 7^3 + 17^3 + 23^3 + 27^3  = 11^3 + 13^3 + 21^3 + 29^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025365, A344927, A345120, A345146, A345153, A345156, A345186.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 9])
for x in range(len(rets)):
    print(rets[x])

A345155 Numbers that are the sum of four third powers in ten or more ways.

Original entry on oeis.org

21896, 36225, 46872, 48321, 48825, 51506, 52416, 53200, 55575, 58338, 58968, 59059, 60480, 62244, 66024, 67536, 67851, 70434, 70525, 71155, 72819, 73808, 76384, 76923, 77896, 78624, 78912, 81081, 81991, 85995, 87507, 88641, 90181, 90783, 91448, 91728, 92008

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			21896 is a term because 21896 = 1^3 + 11^3 + 19^3 + 22^3  = 2^3 + 2^3 + 12^3 + 26^3  = 2^3 + 3^3 + 19^3 + 23^3  = 2^3 + 5^3 + 15^3 + 25^3  = 3^3 + 10^3 + 16^3 + 24^3  = 3^3 + 17^3 + 19^3 + 19^3  = 4^3 + 6^3 + 20^3 + 22^3  = 5^3 + 8^3 + 14^3 + 25^3  = 7^3 + 11^3 + 17^3 + 23^3  = 8^3 + 9^3 + 19^3 + 22^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025375, A344928, A345121, A345146, A345156, A345187.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
    print(rets[x])

A025374 Numbers that are the sum of 4 nonzero squares in 9 or more ways.

Original entry on oeis.org

162, 178, 198, 202, 207, 210, 220, 223, 225, 226, 231, 234, 242, 243, 246, 247, 250, 252, 253, 255, 258, 262, 265, 266, 267, 268, 270, 271, 273, 274, 278, 279, 282, 283, 285, 286, 287, 290, 291, 292, 294, 295, 297, 298, 300, 301, 303, 306, 307, 309, 310, 313, 314, 315

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025337, A025365, A025373, A025375, A344802, A345146.

{n: A025428(n) >= 9}. - R. J. Mathar, Jun 15 2018

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A345152 Numbers that are the sum of four third powers in eight or more ways.

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A345119 Numbers that are the sum of three third powers in nine or more ways.

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A345185 Numbers that are the sum of five third powers in nine or more ways.

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A344926 Numbers that are the sum of four fourth powers in nine or more ways.

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A345154 Numbers that are the sum of four third powers in exactly nine ways.

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A345155 Numbers that are the sum of four third powers in ten or more ways.

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A025374 Numbers that are the sum of 4 nonzero squares in 9 or more ways.

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