A345155 -id:A345155 - cp's OEIS frontend

A345146 Numbers that are the sum of four third powers in nine or more ways.

21896, 36225, 42120, 46683, 46872, 48321, 48825, 50806, 50904, 51408, 51480, 51506, 51688, 52208, 52416, 53200, 53865, 54971, 55575, 56385, 57113, 58338, 58968, 59059, 60480, 60515, 60984, 62244, 62433, 65303, 66024, 66276, 66339, 66430, 67158, 67536, 67851

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			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. A025374, A344926, A345119, A345152, A345154, A345155, A345185.

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])

A025375 Numbers that are the sum of 4 nonzero squares in 10 or more ways.

Original entry on oeis.org

198, 202, 210, 234, 246, 247, 250, 252, 255, 258, 262, 268, 270, 273, 274, 279, 282, 285, 290, 292, 294, 295, 297, 298, 300, 301, 303, 306, 307, 310, 313, 315, 318, 319, 322, 324, 325, 327, 330, 333, 335, 338, 339, 340, 342, 343, 345, 346, 348, 350, 351, 354, 355, 357

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025338, A025366, A025374, A344803, A345155.

{n: A025428(n) >= 10}. - R. J. Mathar, Jun 15 2018

A345187 Numbers that are the sum of five third powers in ten or more ways.

Original entry on oeis.org

5860, 6588, 6651, 6859, 6947, 8056, 8289, 8371, 8506, 8569, 8758, 9045, 9080, 9099, 9108, 9227, 9414, 9612, 9801, 9829, 9864, 10009, 10018, 10044, 10277, 10466, 10485, 10522, 10529, 10800, 10963, 10970, 10979, 11008, 11017, 11061, 11089, 11152, 11241, 11385

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			6588 is a term because 6588 = 1^3 + 3^3 + 5^3 + 7^3 + 17^3  = 1^3 + 4^3 + 6^3 + 13^3 + 14^3  = 1^3 + 5^3 + 8^3 + 8^3 + 16^3  = 1^3 + 10^3 + 10^3 + 11^3 + 12^3  = 2^3 + 2^3 + 9^3 + 12^3 + 14^3  = 2^3 + 3^3 + 8^3 + 11^3 + 15^3  = 3^3 + 8^3 + 8^3 + 11^3 + 14^3  = 3^3 + 3^3 + 5^3 + 10^3 + 16^3  = 5^3 + 5^3 + 8^3 + 10^3 + 15^3  = 8^3 + 9^3 + 10^3 + 10^3 + 12^3.

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

Cf. A341897, A344803, A345155, A345185, A345188, A345519.

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 >= 10])
for x in range(len(rets)):
    print(rets[x])

A344928 Numbers that are the sum of four fourth powers in ten or more ways.

Original entry on oeis.org

592417938, 677125218, 780595299, 781388643, 803898018, 806692194, 937239954, 940415058, 980421939, 1164012003, 1269819378, 1355899923, 1403089314, 1488645939, 1539221154, 1599073938, 1635878754, 1657885698, 1666044963, 1701067683, 1734489603, 1758151458

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

			592417938 is a term because 592417938 = 6^4 + 59^4 + 65^4 + 154^4  = 7^4 + 11^4 + 20^4 + 156^4  = 10^4 + 17^4 + 17^4 + 156^4  = 12^4 + 112^4 + 115^4 + 127^4  = 15^4 + 86^4 + 107^4 + 142^4  = 21^4 + 49^4 + 70^4 + 154^4  = 25^4 + 107^4 + 112^4 + 132^4  = 26^4 + 45^4 + 71^4 + 154^4  = 28^4 + 105^4 + 112^4 + 133^4  = 63^4 + 77^4 + 112^4 + 140^4.

Sean A. Irvine, Table of n, a(n) for n = 1..2061

Cf. A341897, A344862, A344926, A344929, A345155.

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 >= 10])
for x in range(len(rets)):
    print(rets[x])

More terms from Sean A. Irvine, Jun 03 2021

A345121 Numbers that are the sum of three third powers in ten or more ways.

Original entry on oeis.org

34012224, 58995000, 69190848, 71319312, 72505152, 92853216, 94118760, 95331816, 119095488, 119409984, 139755888, 147545280, 150506000, 150547032, 157464000, 159874560, 161023680, 161350272, 164186352, 171904032, 175986000, 176175000, 182393856, 184909824

Offset: 1

David Consiglio, Jr., Jun 08 2021

nonn

			34012224 is a term because 34012224 = 35^3 + 215^3 + 287^3  = 38^3 + 152^3 + 311^3  = 40^3 + 113^3 + 318^3  = 44^3 + 245^3 + 266^3  = 71^3 + 113^3 + 317^3  = 99^3 + 191^3 + 295^3  = 101^3 + 226^3 + 276^3  = 117^3 + 185^3 + 295^3  = 161^3 + 215^3 + 269^3  = 172^3 + 213^3 + 266^3.

Sean A. Irvine, Table of n, a(n) for n = 1..3429

Cf. A025338, A344862, A345119, A345122, A345155.

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 >= 10])
for x in range(len(rets)):
    print(rets[x])

More terms from Sean A. Irvine, Jun 08 2021

A345156 Numbers that are the sum of four third powers in exactly ten ways.

Original entry on oeis.org

21896, 36225, 48825, 51506, 52416, 53200, 58338, 58968, 60480, 66024, 67851, 70434, 70525, 71155, 72819, 76923, 78624, 78912, 85995, 87507, 88641, 90181, 90783, 91728, 93555, 97552, 98280, 98560, 99008, 99225, 99792, 100170, 103040, 104104, 104265, 104958

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345155 at term 3 because 46872 = 1^3 + 16^3 + 22^3 + 30^3 = 2^3 + 11^3 + 17^3 + 33^3 = 3^3 + 3^3 + 4^3 + 35^3 = 3^3 + 4^3 + 26^3 + 29^3 = 3^3 + 5^3 + 23^3 + 31^3 = 4^3 + 10^3 + 24^3 + 30^3 = 5^3 + 17^3 + 23^3 + 29^3 = 6^3 + 10^3 + 20^3 + 32^3 = 11^3 + 11^3 + 21^3 + 31^3 = 11^3 + 14^3 + 17^3 + 32^3 = 19^3 + 21^3 + 21^3 + 25^3.

			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. A025366, A344929, A345122, A345154, A345155, A345188.

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])

cp's OEIS Frontend

A345146 Numbers that are the sum of four third powers in nine or more ways.

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A025375 Numbers that are the sum of 4 nonzero squares in 10 or more ways.

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A345187 Numbers that are the sum of five third powers in ten or more ways.

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A344928 Numbers that are the sum of four fourth powers in ten or more ways.

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A345121 Numbers that are the sum of three third powers in ten or more ways.

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A345156 Numbers that are the sum of four third powers in exactly ten ways.

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