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A345621 Numbers that are the sum of nine fifth powers in four or more ways. 7

%I #6 Jul 31 2021 16:09:02

%S 55542,120350,143507,167241,182549,192233,202890,326685,327986,328247,

%T 329028,329809,333257,351722,358474,358968,359210,359538,359813,

%U 365404,367071,367313,374034,374846,375627,376619,377158,379259,381157,383910,384765,390396

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

%H Sean A. Irvine, <a href="/A345621/b345621.txt">Table of n, a(n) for n = 1..10000</a>

%e 120350 is a term because 120350 = 1^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 = 1^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 = 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 7^5 + 7^5 + 9^5 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 6^5 + 8^5 + 9^5.

%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, 9):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 4])

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

%o print(rets[x])

%Y Cf. A345588, A345612, A345620, A345622, A345636, A346339.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021

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