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A345561 Numbers that are the sum of six fourth powers in four or more ways.

%I A345561 #6 Jul 31 2021 18:05:06
%S A345561 6626,6691,6866,9251,9491,10115,10706,10786,11555,12595,14225,14691,
%T A345561 14771,15315,15330,15395,15570,16051,16595,16610,16660,16675,16850,
%U A345561 17090,17091,17236,17316,17331,17346,17860,17875,17940,17955,18195,18786,18851,18866,19155
%N A345561 Numbers that are the sum of six fourth powers in four or more ways.
%H A345561 Sean A. Irvine, <a href="/A345561/b345561.txt">Table of n, a(n) for n = 1..10000</a>
%e A345561 6691 is a term because 6691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4.
%o A345561 (Python)
%o A345561 from itertools import combinations_with_replacement as cwr
%o A345561 from collections import defaultdict
%o A345561 keep = defaultdict(lambda: 0)
%o A345561 power_terms = [x**4 for x in range(1, 1000)]
%o A345561 for pos in cwr(power_terms, 6):
%o A345561     tot = sum(pos)
%o A345561     keep[tot] += 1
%o A345561     rets = sorted([k for k, v in keep.items() if v >= 4])
%o A345561     for x in range(len(rets)):
%o A345561         print(rets[x])
%Y A345561 Cf. A344354, A345513, A345560, A345562, A345570, A345718, A345816.
%K A345561 nonn
%O A345561 1,1
%A A345561 _David Consiglio, Jr._, Jun 20 2021