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A344355 Numbers that are the sum of five fourth powers in exactly four ways.

%I A344355 #12 Jul 31 2021 22:02:56
%S A344355 20995,21235,31250,41474,43235,43250,43315,43490,43859,45139,46290,
%T A344355 47570,51939,53234,53299,54994,56274,57379,57410,57779,59329,63970,
%U A344355 67010,68035,68290,71795,71954,73730,73954,75714,75794,77890,82099,84499,86275,86450,87730,92500,93474,93859,94130,94210,96194
%N A344355 Numbers that are the sum of five fourth powers in exactly four ways.
%C A344355 Differs from A344354 at term 22 because 59779 = 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 7^4 + 7^4 + 9^4 + 10^4 + 14^4.
%H A344355 David Consiglio, Jr., <a href="/A344355/b344355.txt">Table of n, a(n) for n = 1..20000</a>
%e A344355 31250 is a term of this sequence because 31250 = 2^4 + 2^4 + 4^4 + 7^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 13^4 = 4^4 + 6^4 + 7^4 + 9^4 + 12^4 = 5^4 + 5^4 + 10^4 + 10^4 + 10^4.
%o A344355 (Python)
%o A344355 from itertools import combinations_with_replacement as cwr
%o A344355 from collections import defaultdict
%o A344355 keep = defaultdict(lambda: 0)
%o A344355 power_terms = [x**4 for x in range(1, 50)]
%o A344355 for pos in cwr(power_terms, 5):
%o A344355     tot = sum(pos)
%o A344355     keep[tot] += 1
%o A344355 rets = sorted([k for k, v in keep.items() if v == 4])
%o A344355 for x in range(len(rets)):
%o A344355     print(rets[x])
%Y A344355 Cf. A344035, A344244, A344353, A344354, A344359, A344519, A345816.
%K A344355 nonn
%O A344355 1,1
%A A344355 _David Consiglio, Jr._, May 15 2021