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A345723
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Numbers that are the sum of six fifth powers in nine or more ways.
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6
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9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 55302546200, 56229189632, 57088402525, 59954496800, 63432407850
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OFFSET
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1,1
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LINKS
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EXAMPLE
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16933805856 = 2^5 + 38^5 + 68^5 + 74^5 + 92^5 + 92^5
= 2^5 + 54^5 + 58^5 + 64^5 + 92^5 + 96^5
= 14^5 + 36^5 + 61^5 + 67^5 + 94^5 + 94^5
= 15^5 + 49^5 + 52^5 + 60^5 + 94^5 + 96^5
= 17^5 + 49^5 + 53^5 + 57^5 + 92^5 + 98^5
= 29^5 + 36^5 + 42^5 + 72^5 + 88^5 + 99^5
= 31^5 + 36^5 + 54^5 + 54^5 + 94^5 + 97^5
= 34^5 + 34^5 + 46^5 + 72^5 + 76^5 + 104^5
= 35^5 + 36^5 + 69^5 + 72^5 + 89^5 + 95^5
so 16933805856 is a term.
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PROG
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(Python)
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 >= 9])
for x in range(len(rets)):
print(rets[x])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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