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A346364 Numbers that are the sum of six fifth powers in exactly nine ways.

%I A346364 #11 May 11 2024 20:43:37
%S A346364 9085584992,16933805856,37377003050,39254220544,41066625600,
%T A346364 41485873792,42149876800,43828403850,44180505600,45902654525,
%U A346364 48588434400,52005184992,53536896864,54156285568,56229189632,57088402525,59954496800,63432407850,66188522400,66507304800
%N A346364 Numbers that are the sum of six fifth powers in exactly nine ways.
%C A346364 This sequence differs from A345723:
%C A346364 55302546200 = 34^5 + 38^5 + 50^5 +  57^5 +  95^5 + 136^5
%C A346364             = 23^5 + 49^5 + 61^5 +  69^5 + 107^5 + 131^5
%C A346364             = 24^5 + 37^5 + 63^5 +  81^5 + 104^5 + 131^5
%C A346364             = 21^5 + 35^5 + 60^5 +  94^5 + 100^5 + 130^5
%C A346364             = 57^5 + 60^5 + 71^5 +  75^5 + 109^5 + 128^5
%C A346364             = 19^5 + 37^5 + 56^5 +  96^5 + 104^5 + 128^5
%C A346364             = 35^5 + 41^5 + 53^5 +  69^5 + 115^5 + 127^5
%C A346364             = 16^5 + 49^5 + 53^5 +  83^5 + 112^5 + 127^5
%C A346364             = 35^5 + 37^5 + 40^5 +  88^5 + 119^5 + 121^5
%C A346364             = 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5,
%C A346364 so 55302546200 is in A345723, but is not in this sequence.
%H A346364 Sean A. Irvine, <a href="/A346364/b346364.txt">Table of n, a(n) for n = 1..549</a>
%e A346364 9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
%e A346364            = 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
%e A346364            =  8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
%e A346364            = 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
%e A346364            = 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
%e A346364            =  8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
%e A346364            =  5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
%e A346364            =  8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
%e A346364            = 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
%e A346364 so 9085584992 is a term.
%o A346364 (Python)
%o A346364 from itertools import combinations_with_replacement as cwr
%o A346364 from collections import defaultdict
%o A346364 keep = defaultdict(lambda: 0)
%o A346364 power_terms = [x**5 for x in range(1, 1000)]
%o A346364 for pos in cwr(power_terms, 6):
%o A346364     tot = sum(pos)
%o A346364     keep[tot] += 1
%o A346364     rets = sorted([k for k, v in keep.items() if v == 9])
%o A346364     for x in range(len(rets)):
%o A346364         print(rets[x])
%Y A346364 Cf. A345723, A345821, A346286, A346363, A346365.
%K A346364 nonn
%O A346364 1,1
%A A346364 _David Consiglio, Jr._, Jul 13 2021