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A346257 Numbers that are the sum of five fifth powers in exactly five ways.

%I A346257 #6 Jul 31 2021 19:36:15
%S A346257 9006349824,65799210368,67629776576,181085909632,188189635424,
%T A346257 295677350451,467139768468,471359089024,656243139157,691381929281,
%U A346257 797466940832,854533526901,874953049024,891862586132,953769598750,1038549256768,1092458681568,1182658308657
%N A346257 Numbers that are the sum of five fifth powers in exactly five ways.
%C A346257 Differs from 103 terms known at term 6 because 288203194368 = 48^5 + 84^5 + 96^5 + 108^5 + 192^5 = 16^5 + 99^5 + 103^5 + 121^5 + 189^5 = 42^5 + 68^5 + 86^5 + 148^5 + 184^5 = 16^5 + 68^5 + 124^5 + 136^5 + 184^5 = 16^5 + 82^5 + 94^5 + 158^5 + 178^5 = 24^5 + 36^5 + 144^5 + 156^5 + 168^5.
%H A346257 Sean A. Irvine, <a href="/A346257/b346257.txt">Table of n, a(n) for n = 1..253</a>
%e A346257 9006349824 is a term because 9006349824 = 24^5 + 42^5 + 48^5 + 54^5 + 96^5 = 21^5 + 34^5 + 43^5 + 74^5 + 92^5 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5 = 8^5 + 41^5 + 47^5 + 79^5 + 89^5 = 12^5 + 18^5 + 72^5 + 78^5 + 84^5.
%o A346257 (Python)
%o A346257 from itertools import combinations_with_replacement as cwr
%o A346257 from collections import defaultdict
%o A346257 keep = defaultdict(lambda: 0)
%o A346257 power_terms = [x**5 for x in range(1, 1000)]
%o A346257 for pos in cwr(power_terms, 5):
%o A346257     tot = sum(pos)
%o A346257     keep[tot] += 1
%o A346257     rets = sorted([k for k, v in keep.items() if v == 5])
%o A346257     for x in range(len(rets)):
%o A346257         print(rets[x])
%Y A346257 Cf. A344359, A344519, A345863, A346360.
%K A346257 nonn
%O A346257 1,1
%A A346257 _David Consiglio, Jr._, Jul 11 2021