A345087
Numbers that are the sum of three third powers in eight or more ways.
Original entry on oeis.org
2562624, 5618250, 6525000, 6755328, 7374375, 12742920, 13581352, 14027112, 14288373, 14926248, 16819704, 18443160, 20168784, 20500992, 22783032, 23113728, 25305048, 26936064, 27131840, 29515968, 30205440, 32835375, 34012224, 38269440, 39317832, 39339000
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.
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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 >= 8])
for x in range(len(rets)):
print(rets[x])
A344924
Numbers that are the sum of four fourth powers in eight or more ways.
Original entry on oeis.org
13155858, 26421474, 35965458, 39803778, 98926434, 128198994, 143776179, 156279618, 210493728, 237073554, 248075538, 255831858, 257931378, 269965938, 270289698, 292967619, 293579874, 295880274, 300120003, 301080243, 302115843, 305670834, 309742434, 328118259
Offset: 1
13155858 is a term because 13155858 = 1^4 + 16^4 + 19^4 + 60^4 = 3^4 + 6^4 + 21^4 + 60^4 = 10^4 + 18^4 + 31^4 + 59^4 = 12^4 + 27^4 + 45^4 + 54^4 = 15^4 + 44^4 + 46^4 + 47^4 = 18^4 + 25^4 + 41^4 + 56^4 = 29^4 + 30^4 + 44^4 + 53^4 = 35^4 + 36^4 + 38^4 + 53^4.
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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 >= 8])
for x in range(len(rets)):
print(rets[x])
A344729
Numbers that are the sum of three fourth powers in seven or more ways.
Original entry on oeis.org
779888018, 5745705602, 8185089458, 11054952818, 12478208288, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 33038379458, 37314202562, 38214512882, 41923075922, 46543615202, 49511121842, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63170929458, 63429959138, 71035097042, 71447292098, 73526154338, 73665805122, 81629817458
Offset: 1
779888018 is a term because 779888018 = 3^4+ 139^4+ 142^4 = 9^4+ 38^4+ 167^4 = 14^4+ 133^4+ 147^4 = 43^4+ 114^4+ 157^4 = 47^4+ 111^4+ 158^4 = 63^4+ 98^4+ 161^4 = 73^4+ 89^4+ 162^4
-
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 >= 7])
for x in range(len(rets)):
print(rets[x])
A344738
Numbers that are the sum of three fourth powers in exactly eight ways.
Original entry on oeis.org
5745705602, 8185089458, 11054952818, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 37314202562, 38214512882, 41923075922, 46543615202, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63429959138, 71035097042
Offset: 1
5745705602 is a term because 5745705602 = 3^4 + 230^4 + 233^4 = 25^4 + 218^4 + 243^4 = 43^4 + 207^4 + 250^4 = 58^4 + 197^4 + 255^4 = 85^4 + 177^4 + 262^4 = 90^4 + 173^4 + 263^4 = 102^4 + 163^4 + 265^4 = 122^4 + 145^4 + 267^4.
-
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 == 8])
for x in range(len(rets)):
print(rets[x])
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.
-
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])
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