A345723 - OEIS

%I #10 May 10 2024 02:41:51

%S 9085584992,16933805856,37377003050,39254220544,41066625600,

%T 41485873792,42149876800,43828403850,44180505600,45902654525,

%U 48588434400,52005184992,53536896864,54156285568,55302546200,56229189632,57088402525,59954496800,63432407850

%N Numbers that are the sum of six fifth powers in nine or more ways.

%H Sean A. Irvine, <a href="/A345723/b345723.txt">Table of n, a(n) for n = 1..127</a>

%e 16933805856 =  2^5 + 38^5 + 68^5 + 74^5 + 92^5 +  92^5

%e             =  2^5 + 54^5 + 58^5 + 64^5 + 92^5 +  96^5

%e             = 14^5 + 36^5 + 61^5 + 67^5 + 94^5 +  94^5

%e             = 15^5 + 49^5 + 52^5 + 60^5 + 94^5 +  96^5

%e             = 17^5 + 49^5 + 53^5 + 57^5 + 92^5 +  98^5

%e             = 29^5 + 36^5 + 42^5 + 72^5 + 88^5 +  99^5

%e             = 31^5 + 36^5 + 54^5 + 54^5 + 94^5 +  97^5

%e             = 34^5 + 34^5 + 46^5 + 72^5 + 76^5 + 104^5

%e             = 35^5 + 36^5 + 69^5 + 72^5 + 89^5 +  95^5

%e so 16933805856 is a term.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**5 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 6):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v >= 9])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A344196, A345566, A345631, A345722, A346364.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 24 2021