A344751
Numbers that are the sum of three fourth powers in exactly nine ways.
Original entry on oeis.org
105760443698, 131801075042, 187758243218, 253590205778, 319889609522, 445600096578, 510334859762, 601395185762, 615665999858, 730871934338, 749472385298, 855952663202, 856722174098, 951843993282, 1157106866258, 1186209675378, 1290443616098, 1455023522498
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])
A344929
Numbers that are the sum of four fourth powers in exactly ten ways.
Original entry on oeis.org
592417938, 806692194, 940415058, 980421939, 1269819378, 1355899923, 1488645939, 1599073938, 1635878754, 1657885698, 1666044963, 1758151458, 1797373314, 1813434483, 1991146899, 2064726483, 2198975058, 2246905683, 2266525314, 2302589298, 2302698258, 2502041283
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])
A344862
Numbers that are the sum of three fourth powers in ten or more ways.
Original entry on oeis.org
49511121842, 281539574498, 364765611938, 401069383442, 541692688082, 703409488418, 792177949472, 971024246738, 1067666696642, 1090123576178, 1315120863602, 1383280118402, 1442012945282, 1561211646722, 1828395925538, 1868287026242, 1872511131218, 2054230720178
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])
A345122
Numbers that are the sum of three third powers in exactly ten ways.
Original entry on oeis.org
34012224, 58995000, 71319312, 72505152, 92853216, 94118760, 95331816, 139755888, 147545280, 150506000, 157464000, 159874560, 161023680, 164186352, 171904032, 182393856, 184909824, 188224128, 189771336, 191260224, 199108125, 201342240, 202440384, 217054720
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.
-
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])
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