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A344359 Numbers that are the sum of five fourth powers in exactly five ways.

%I A344359 #14 Jul 31 2021 22:02:59
%S A344359 59779,67859,93394,108274,112850,136915,142354,151475,161459,168979,
%T A344359 181219,183539,183604,185299,187699,189394,193379,195394,199090,
%U A344359 199474,200979,201874,202979,203299,205859,211330,212419,213730,217810,217890,221779,223090,223155,223714,226514,227779,231235
%N A344359 Numbers that are the sum of five fourth powers in exactly five ways.
%C A344359 Differs from A344358 at term 8 because 151300 = 3^4 + 3^4 + 3^4 + 12^4 + 19^4 = 3^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 13^4 + 13^4 + 13^4 + 16^4 = 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 8^4 + 9^4 + 13^4 + 13^4 + 17^4.
%H A344359 David Consiglio, Jr., <a href="/A344359/b344359.txt">Table of n, a(n) for n = 1..20000</a>
%e A344359 93394 is a term of this sequence because 93394 = 1^4 + 4^4 + 8^4 + 14^4 + 15^4 = 1^4 + 6^4 + 12^4 + 12^4 + 15^4 = 1^4 + 9^4 + 10^4 + 14^4 + 14^4 = 5^4 + 6^4 + 11^4 + 14^4 + 14^4 = 5^4 + 7^4 + 8^4 + 12^4 + 16^4.
%o A344359 (Python)
%o A344359 from itertools import combinations_with_replacement as cwr
%o A344359 from collections import defaultdict
%o A344359 keep = defaultdict(lambda: 0)
%o A344359 power_terms = [x**4 for x in range(1, 50)]
%o A344359 for pos in cwr(power_terms, 5):
%o A344359     tot = sum(pos)
%o A344359     keep[tot] += 1
%o A344359 rets = sorted([k for k, v in keep.items() if v == 5])
%o A344359 for x in range(len(rets)):
%o A344359     print(rets[x])
%Y A344359 Cf. A343988, A344355, A344357, A344358, A344941, A345817, A346257.
%K A344359 nonn
%O A344359 1,1
%A A344359 _David Consiglio, Jr._, May 15 2021