A345120
Numbers that are the sum of three third powers in exactly nine ways.
Original entry on oeis.org
14926248, 16819704, 20168784, 44946000, 45580536, 54042624, 59768064, 62099136, 66203136, 67956624, 69393024, 78008832, 78716448, 79539832, 80621568, 80996544, 89354448, 90757584, 99616392, 100088568, 101352168, 101943360, 112216896, 112720896, 114306984
Offset: 1
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.
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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 == 9])
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.
-
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])
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
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.
-
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])
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])
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