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%I #10 Jul 31 2021 22:02:39
%S 619090,775714,1100579,1179379,1186834,1243699,1357315,1367539,
%T 1373859,1422595,1431234,1436419,1511299,1536019,1699234,1734899,
%U 1839874,1858594,1880850,1950355,1951650,1978915,2044819,2052899,2069955,2085139,2101779,2119459,2133234
%N Numbers that are the sum of five fourth powers in exactly nine ways.
%C Differs from A341781 at term 3 because 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.
%H David Consiglio, Jr., <a href="/A341892/b341892.txt">Table of n, a(n) for n = 1..10000</a>
%e 619090 is a term because 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.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**4 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 5):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 9])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A341891, A341898, A344927, A344945, A345186, A345821.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 04 2021
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