

A345562


Numbers that are the sum of six fourth powers in five or more ways.


8



15395, 16610, 18866, 19235, 19410, 20996, 21011, 21251, 21316, 21331, 21491, 21620, 23811, 25091, 29700, 29715, 29906, 29955, 30356, 30995, 31235, 31266, 31331, 31506, 32035, 33651, 33795, 33891, 35171, 35411, 35636, 35796, 35971, 37811, 37971, 38051, 38595
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OFFSET

1,1


LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..10000


EXAMPLE

16610 is a term because 16610 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 10^4 = 2^4 + 2^4 + 2^4 + 5^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 10^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.


PROG

(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, 6):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 5])
for x in range(len(rets)):
print(rets[x])


CROSSREFS

Cf. A344358, A345514, A345561, A345563, A345571, A345719, A345817.
Sequence in context: A182255 A054836 A054837 * A345817 A252990 A252842
Adjacent sequences: A345559 A345560 A345561 * A345563 A345564 A345565


KEYWORD

nonn


AUTHOR

David Consiglio, Jr., Jun 20 2021


STATUS

approved



