cp's OEIS Frontend

A346351 Numbers that are the sum of ten fifth powers in exactly six ways.

%I A346351 #6 Jul 31 2021 18:54:16
%S A346351 392095,392306,399839,406802,407583,434676,491643,492063,520261,
%T A346351 521106,538323,538534,540927,553325,563526,582089,592398,608190,
%U A346351 611072,614196,637833,639903,640715,640895,640926,640957,641106,643671,653523,655327,656616,664895
%N A346351 Numbers that are the sum of ten fifth powers in exactly six ways.
%C A346351 Differs from A345638 at term 15 because 555098 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 7^5 + 14^5 = 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 7^5 + 8^5 + 10^5 + 13^5 = 1^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 7^5 + 10^5 + 13^5 = 1^5 + 2^5 + 5^5 + 7^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 13^5 = 4^5 + 4^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 11^5 + 12^5 = 3^5 + 3^5 + 4^5 + 4^5 + 6^5 + 7^5 + 9^5 + 9^5 + 11^5 + 12^5 = 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 + 11^5.
%H A346351 Sean A. Irvine, <a href="/A346351/b346351.txt">Table of n, a(n) for n = 1..10000</a>
%e A346351 392095 is a term because 392095 = 2^5 + 2^5 + 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 1^5 + 1^5 + 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 7^5 + 10^5 + 12^5 = 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 2^5 + 2^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5.
%o A346351 (Python)
%o A346351 from itertools import combinations_with_replacement as cwr
%o A346351 from collections import defaultdict
%o A346351 keep = defaultdict(lambda: 0)
%o A346351 power_terms = [x**5 for x in range(1, 1000)]
%o A346351 for pos in cwr(power_terms, 10):
%o A346351     tot = sum(pos)
%o A346351     keep[tot] += 1
%o A346351     rets = sorted([k for k, v in keep.items() if v == 6])
%o A346351     for x in range(len(rets)):
%o A346351         print(rets[x])
%Y A346351 Cf. A345638, A345858, A346341, A346350, A346352.
%K A346351 nonn
%O A346351 1,1
%A A346351 _David Consiglio, Jr._, Jul 13 2021