cp's OEIS Frontend

A346333 Numbers that are the sum of eight fifth powers in exactly eight ways.

%I A346333 #6 Jul 31 2021 19:04:02
%S A346333 8625619,9773236,10036233,10071050,12247994,13180706,13377868,
%T A346333 13662501,14584992,14591744,14611077,15251119,16112362,16374250,
%U A346333 16391025,16472544,16588000,16667851,17059075,17216298,17405300,17917097,18107564,18392902,18470839,18541635
%N A346333 Numbers that are the sum of eight fifth powers in exactly eight ways.
%C A346333 Differs from A345616 at term 2 because 8742208 = 1^5 + 1^5 + 2^5 + 3^5 + 5^5 + 7^5 + 15^5 + 24^5 = 4^5 + 4^5 + 8^5 + 8^5 + 9^5 + 15^5 + 17^5 + 23^5 = 1^5 + 3^5 + 7^5 + 12^5 + 12^5 + 13^5 + 17^5 + 23^5 = 2^5 + 5^5 + 6^5 + 7^5 + 15^5 + 15^5 + 15^5 + 23^5 = 1^5 + 1^5 + 9^5 + 9^5 + 11^5 + 17^5 + 18^5 + 22^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 12^5 + 21^5 + 21^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 12^5 + 21^5 + 21^5 = 10^5 + 12^5 + 12^5 + 13^5 + 16^5 + 16^5 + 19^5 + 20^5 = 8^5 + 13^5 + 14^5 + 14^5 + 14^5 + 16^5 + 19^5 + 20^5.
%H A346333 Sean A. Irvine, <a href="/A346333/b346333.txt">Table of n, a(n) for n = 1..10000</a>
%e A346333 8625619 is a term because 8625619 = 2^5 + 5^5 + 5^5 + 9^5 + 10^5 + 12^5 + 12^5 + 24^5 = 1^5 + 3^5 + 8^5 + 9^5 + 11^5 + 11^5 + 12^5 + 24^5 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 16^5 + 16^5 + 23^5 = 1^5 + 3^5 + 3^5 + 4^5 + 11^5 + 17^5 + 18^5 + 22^5 = 4^5 + 11^5 + 13^5 + 13^5 + 15^5 + 15^5 + 16^5 + 22^5 = 5^5 + 6^5 + 13^5 + 15^5 + 15^5 + 16^5 + 19^5 + 20^5 = 3^5 + 10^5 + 12^5 + 12^5 + 16^5 + 18^5 + 18^5 + 20^5 = 3^5 + 8^5 + 14^5 + 14^5 + 14^5 + 18^5 + 18^5 + 20^5.
%o A346333 (Python)
%o A346333 from itertools import combinations_with_replacement as cwr
%o A346333 from collections import defaultdict
%o A346333 keep = defaultdict(lambda: 0)
%o A346333 power_terms = [x**5 for x in range(1, 1000)]
%o A346333 for pos in cwr(power_terms, 8):
%o A346333     tot = sum(pos)
%o A346333     keep[tot] += 1
%o A346333     rets = sorted([k for k, v in keep.items() if v == 8])
%o A346333     for x in range(len(rets)):
%o A346333         print(rets[x])
%Y A346333 Cf. A345616, A345840, A346285, A346332, A346334, A346343.
%K A346333 nonn
%O A346333 1,1
%A A346333 _David Consiglio, Jr._, Jul 13 2021