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
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])
A345088
Numbers that are the sum of three third powers in exactly eight ways.
Original entry on oeis.org
2562624, 5618250, 6525000, 6755328, 7374375, 12742920, 13581352, 14027112, 14288373, 18443160, 20500992, 22783032, 23113728, 25305048, 26936064, 27131840, 29515968, 30205440, 32835375, 38269440, 39317832, 39339000, 40189248, 42144192, 42183504, 43077952
Offset: 1
2562624 is a term because 2562624 = 7^3 + 35^3 + 135^3 = 7^3 + 63^3 + 131^3 = 11^3 + 99^3 + 115^3 = 16^3 + 45^3 + 134^3 = 29^3 + 102^3 + 112^3 = 35^3 + 59^3 + 131^3 = 50^3 + 84^3 + 121^3 = 68^3 + 71^3 + 122^3.
-
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 == 8])
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
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.
-
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])
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])
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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