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A341897
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Numbers that are the sum of five fourth powers in ten or more ways.
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6
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954979, 1205539, 1574850, 1713859, 1801459, 1863859, 1877394, 1882579, 2071939, 2109730, 2138419, 2142594, 2157874, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2663539, 2711394, 2784499, 2835939, 2847394, 2849859, 2880994, 2919154, 2924674, 3007474
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listen;
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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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954979 = 1^4 + 2^4 + 11^4 + 19^4 + 30^4
= 1^4 + 7^4 + 18^4 + 25^4 + 26^4
= 3^4 + 8^4 + 17^4 + 20^4 + 29^4
= 4^4 + 8^4 + 13^4 + 25^4 + 27^4
= 4^4 + 9^4 + 10^4 + 11^4 + 31^4
= 6^4 + 6^4 + 15^4 + 21^4 + 29^4
= 7^4 + 10^4 + 18^4 + 19^4 + 29^4
= 11^4 + 11^4 + 20^4 + 22^4 + 27^4
= 16^4 + 17^4 + 17^4 + 24^4 + 25^4
= 18^4 + 19^4 + 20^4 + 23^4 + 23^4
so 954979 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**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 >= 10])
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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