A341892
Numbers that are the sum of five fourth powers in exactly nine ways.
Original entry on oeis.org
619090, 775714, 1100579, 1179379, 1186834, 1243699, 1357315, 1367539, 1373859, 1422595, 1431234, 1436419, 1511299, 1536019, 1699234, 1734899, 1839874, 1858594, 1880850, 1950355, 1951650, 1978915, 2044819, 2052899, 2069955, 2085139, 2101779, 2119459, 2133234
Offset: 1
619090 = 1^4 + 2^4 + 18^4 + 22^4 + 23^4
= 1^4 + 3^4 + 4^4 + 8^4 + 28^4
= 1^4 + 11^4 + 14^4 + 22^4 + 24^4
= 2^4 + 2^4 + 8^4 + 17^4 + 27^4
= 2^4 + 13^4 + 13^4 + 18^4 + 26^4
= 3^4 + 6^4 + 12^4 + 16^4 + 27^4
= 4^4 + 12^4 + 14^4 + 23^4 + 23^4
= 9^4 + 12^4 + 16^4 + 21^4 + 24^4
= 14^4 + 16^4 + 18^4 + 19^4 + 23^4
so 619090 is a term.
-
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, 5):
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])
A344925
Numbers that are the sum of four fourth powers in exactly eight 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, 331957458
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.
-
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])
A344926
Numbers that are the sum of four fourth powers in nine or more ways.
Original entry on oeis.org
328118259, 385202034, 395613234, 489597858, 592417938, 625839858, 641398338, 674511618, 677125218, 693239634, 699598578, 722302434, 779889314, 780278643, 780595299, 781388643, 782999714, 791204514, 792005379, 797405714, 797935698, 803898018, 805299699
Offset: 1
328118259 is a term because 328118259 = 2^4 + 77^4 + 109^4 + 111^4 = 8^4 + 79^4 + 93^4 + 121^4 = 18^4 + 79^4 + 97^4 + 119^4 = 21^4 + 77^4 + 98^4 + 119^4 = 27^4 + 77^4 + 94^4 + 121^4 = 34^4 + 77^4 + 89^4 + 123^4 = 46^4 + 57^4 + 103^4 + 119^4 = 49^4 + 77^4 + 77^4 + 126^4 = 61^4 + 66^4 + 77^4 + 127^4.
-
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, 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])
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.
-
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.
-
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])
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