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A341892 Numbers that are the sum of five fourth powers in exactly nine ways.

%I A341892 #14 May 10 2024 02:27:25
%S A341892 619090,775714,1100579,1179379,1186834,1243699,1357315,1367539,
%T A341892 1373859,1422595,1431234,1436419,1511299,1536019,1699234,1734899,
%U A341892 1839874,1858594,1880850,1950355,1951650,1978915,2044819,2052899,2069955,2085139,2101779,2119459,2133234
%N A341892 Numbers that are the sum of five fourth powers in exactly nine ways.
%C A341892 Differs from A341781 at term 3 because
%C A341892 954979 =  1^4 +  2^4 + 11^4 + 19^4 + 30^4
%C A341892        =  1^4 +  7^4 + 18^4 + 25^4 + 26^4
%C A341892        =  3^4 +  8^4 + 17^4 + 20^4 + 29^4
%C A341892        =  4^4 +  8^4 + 13^4 + 25^4 + 27^4
%C A341892        =  4^4 +  9^4 + 10^4 + 11^4 + 31^4
%C A341892        =  6^4 +  6^4 + 15^4 + 21^4 + 29^4
%C A341892        =  7^4 + 10^4 + 18^4 + 19^4 + 29^4
%C A341892        = 11^4 + 11^4 + 20^4 + 22^4 + 27^4
%C A341892        = 16^4 + 17^4 + 17^4 + 24^4 + 25^4
%C A341892        = 18^4 + 19^4 + 20^4 + 23^4 + 23^4.
%H A341892 David Consiglio, Jr., <a href="/A341892/b341892.txt">Table of n, a(n) for n = 1..10000</a>
%e A341892 619090 =  1^4 +  2^4 + 18^4 + 22^4 + 23^4
%e A341892        =  1^4 +  3^4 +  4^4 +  8^4 + 28^4
%e A341892        =  1^4 + 11^4 + 14^4 + 22^4 + 24^4
%e A341892        =  2^4 +  2^4 +  8^4 + 17^4 + 27^4
%e A341892        =  2^4 + 13^4 + 13^4 + 18^4 + 26^4
%e A341892        =  3^4 +  6^4 + 12^4 + 16^4 + 27^4
%e A341892        =  4^4 + 12^4 + 14^4 + 23^4 + 23^4
%e A341892        =  9^4 + 12^4 + 16^4 + 21^4 + 24^4
%e A341892        = 14^4 + 16^4 + 18^4 + 19^4 + 23^4
%e A341892 so 619090 is a term.
%o A341892 (Python)
%o A341892 from itertools import combinations_with_replacement as cwr
%o A341892 from collections import defaultdict
%o A341892 keep = defaultdict(lambda: 0)
%o A341892 power_terms = [x**4 for x in range(1, 1000)]
%o A341892 for pos in cwr(power_terms, 5):
%o A341892     tot = sum(pos)
%o A341892     keep[tot] += 1
%o A341892 rets = sorted([k for k, v in keep.items() if v == 9])
%o A341892 for x in range(len(rets)):
%o A341892     print(rets[x])
%Y A341892 Cf. A341891, A341898, A344927, A344945, A345186, A345821.
%K A341892 nonn
%O A341892 1,1
%A A341892 _David Consiglio, Jr._, Jun 04 2021