A345564
Numbers that are the sum of six fourth powers in seven or more ways.
Original entry on oeis.org
21251, 43875, 48276, 49796, 53315, 58035, 58500, 59780, 59795, 59811, 67875, 68306, 69155, 69779, 71955, 72051, 72131, 73970, 74420, 74851, 77010, 80291, 80515, 81875, 82275, 84515, 86436, 86451, 86531, 87075, 87746, 88355, 88595, 88660, 88675, 90355, 91475
Offset: 1
43875 is a term because 43875 = 1^4 + 2^4 + 9^4 + 9^4 + 10^4 + 12^4 = 2^4 + 2^4 + 2^4 + 5^4 + 11^4 + 13^4 = 2^4 + 2^4 + 5^4 + 7^4 + 7^4 + 14^4 = 2^4 + 5^4 + 6^4 + 9^4 + 11^4 + 12^4 = 3^4 + 7^4 + 8^4 + 9^4 + 10^4 + 12^4 = 4^4 + 4^4 + 7^4 + 7^4 + 10^4 + 13^4 = 5^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.
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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, 6):
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])
A345629
Numbers that are the sum of seven fifth powers in seven or more ways.
Original entry on oeis.org
28608832, 35663099, 36090526, 36620574, 46998599, 51095638, 52541851, 54233651, 54827543, 54886349, 61263643, 61634374, 63514593, 64810976, 65198607, 66708676, 67887843, 70979107, 72970305, 74002457, 74115801, 74132607, 74487093, 75044651, 75378359
Offset: 1
35663099 is a term because 35663099 = 1^5 + 9^5 + 16^5 + 17^5 + 24^5 + 24^5 + 28^5 = 2^5 + 3^5 + 17^5 + 23^5 + 24^5 + 24^5 + 26^5 = 2^5 + 10^5 + 15^5 + 17^5 + 23^5 + 23^5 + 29^5 = 4^5 + 8^5 + 13^5 + 19^5 + 21^5 + 27^5 + 27^5 = 4^5 + 11^5 + 13^5 + 19^5 + 20^5 + 22^5 + 30^5 = 5^5 + 6^5 + 19^5 + 19^5 + 20^5 + 20^5 + 30^5 = 7^5 + 9^5 + 12^5 + 18^5 + 18^5 + 27^5 + 28^5.
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from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
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])
A345720
Numbers that are the sum of six fifth powers in six or more ways.
Original entry on oeis.org
287718651, 553545456, 746783675, 972232800, 1005620508, 1040741042, 1070652352, 1074892544, 1182426366, 1184966816, 1197332400, 1243267146, 1317183650, 1364866263, 1387455091, 1429663400, 1498160992, 1529189818, 1554833117, 1558594400, 1610298901
Offset: 1
553545456 is a term because 553545456 = 1^5 + 14^5 + 20^5 + 24^5 + 47^5 + 50^5 = 4^5 + 14^5 + 37^5 + 42^5 + 43^5 + 46^5 = 4^5 + 26^5 + 29^5 + 34^5 + 42^5 + 51^5 = 9^5 + 15^5 + 22^5 + 22^5 + 33^5 + 55^5 = 9^5 + 26^5 + 29^5 + 32^5 + 37^5 + 53^5 = 12^5 + 24^5 + 27^5 + 32^5 + 38^5 + 53^5.
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from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 6])
for x in range(len(rets)):
print(rets[x])
A345722
Numbers that are the sum of six fifth powers in eight or more ways.
Original entry on oeis.org
2295937600, 4335900525, 6251954544, 8986552608, 9085584992, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 16933805856, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300
Offset: 1
4335900525 is a term because 4335900525 = 2^5 + 24^5 + 34^5 + 56^5 + 61^5 + 78^5 = 3^5 + 21^5 + 37^5 + 54^5 + 62^5 + 78^5 = 3^5 + 21^5 + 39^5 + 49^5 + 66^5 + 77^5 = 3^5 + 26^5 + 32^5 + 49^5 + 72^5 + 73^5 = 8^5 + 16^5 + 42^5 + 49^5 + 61^5 + 79^5 = 9^5 + 13^5 + 43^5 + 47^5 + 66^5 + 77^5 = 19^5 + 20^5 + 30^5 + 45^5 + 61^5 + 80^5 = 21^5 + 24^5 + 28^5 + 37^5 + 67^5 + 78^5.
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from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
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])
A346362
Numbers that are the sum of six fifth powers in exactly seven ways.
Original entry on oeis.org
1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4489548050, 4539955200, 4623694108, 4710031469
Offset: 1
1184966816 is a term because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.
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from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
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])
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