A344750
Numbers that are the sum of three fourth powers in nine or more ways.
Original entry on oeis.org
49511121842, 105760443698, 131801075042, 187758243218, 253590205778, 281539574498, 319889609522, 364765611938, 401069383442, 445600096578, 510334859762, 541692688082, 601395185762, 615665999858, 703409488418, 730871934338, 749472385298, 792177949472
Offset: 1
105760443698 is a term because 105760443698 = 7^4 + 476^4 + 483^4 = 51^4 + 452^4 + 503^4 = 76^4 + 437^4 + 513^4 = 107^4 + 417^4 + 524^4 = 133^4 + 399^4 + 532^4 = 199^4 + 348^4 + 547^4 = 212^4 + 337^4 + 549^4 = 228^4 + 323^4 + 551^4 = 252^4 + 301^4 + 553^4.
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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, 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])
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
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.
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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])
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
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.
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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])
A344861
Numbers that are the sum of three fourth powers in exactly ten ways.
Original entry on oeis.org
49511121842, 364765611938, 703409488418, 792177949472, 2667500248322, 3602781562562, 3999861055442, 4010400869202, 5698033074818, 5836249791008, 6330685395762, 7250378688098, 7695882509378, 8746828790882, 10383571090802, 11254551814688, 12160605587858
Offset: 1
49511121842 is a term because 49511121842 = 13^4 + 390^4 + 403^4 = 35^4 + 378^4 + 413^4 = 70^4 + 357^4 + 427^4 = 103^4 + 335^4 + 438^4 = 117^4 + 325^4 + 442^4 = 137^4 + 310^4 + 447^4 = 175^4 + 322^4 + 441^4 = 182^4 + 273^4 + 455^4 = 202^4 + 255^4 + 457^4 = 225^4 + 233^4 + 458^4.
-
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, 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])
Showing 1-4 of 4 results.
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