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A341891 Numbers that are the sum of five fourth powers in nine or more ways.

%I A341891 #14 May 10 2024 02:17:19
%S A341891 619090,775714,954979,1100579,1179379,1186834,1205539,1243699,1357315,
%T A341891 1367539,1373859,1422595,1431234,1436419,1511299,1536019,1574850,
%U A341891 1699234,1713859,1734899,1801459,1839874,1858594,1863859,1877394,1880850,1882579,1950355,1951650
%N A341891 Numbers that are the sum of five fourth powers in nine or more ways.
%H A341891 David Consiglio, Jr., <a href="/A341891/b341891.txt">Table of n, a(n) for n = 1..10000</a>
%e A341891 619090 =  1^4 +  2^4 + 18^4 + 22^4 + 23^4
%e A341891        =  1^4 +  3^4 +  4^4 +  8^4 + 28^4
%e A341891        =  1^4 + 11^4 + 14^4 + 22^4 + 24^4
%e A341891        =  2^4 +  2^4 +  8^4 + 17^4 + 27^4
%e A341891        =  2^4 + 13^4 + 13^4 + 18^4 + 26^4
%e A341891        =  3^4 +  6^4 + 12^4 + 16^4 + 27^4
%e A341891        =  4^4 + 12^4 + 14^4 + 23^4 + 23^4
%e A341891        =  9^4 + 12^4 + 16^4 + 21^4 + 24^4
%e A341891        = 14^4 + 16^4 + 18^4 + 19^4 + 23^4
%e A341891 so 619090 is a term.
%o A341891 (Python)
%o A341891 from itertools import combinations_with_replacement as cwr
%o A341891 from collections import defaultdict
%o A341891 keep = defaultdict(lambda: 0)
%o A341891 power_terms = [x**4 for x in range(1, 1000)]
%o A341891 for pos in cwr(power_terms, 5):
%o A341891     tot = sum(pos)
%o A341891     keep[tot] += 1
%o A341891 rets = sorted([k for k, v in keep.items() if v >= 9])
%o A341891 for x in range(len(rets)):
%o A341891     print(rets[x])
%Y A341891 Cf. A341892, A341897, A344926, A344944, A345185, A345566.
%K A341891 nonn
%O A341891 1,1
%A A341891 _David Consiglio, Jr._, Jun 04 2021