cp's OEIS Frontend

A346285 Numbers that are the sum of seven fifth powers in exactly eight ways.

%I A346285 #6 Jul 31 2021 19:12:12
%S A346285 36620574,80552143,81401376,82078424,92347417,93653176,94486699,
%T A346285 94626949,98873875,105674625,121050874,125959393,129228307,144209018,
%U A346285 145340799,147245218,147898763,151727082,151923168,152361276,152664876,153877208,155107349,155270357
%N A346285 Numbers that are the sum of seven fifth powers in exactly eight ways.
%C A346285 Differs from A345630 at term 11 because 110276376 = 1^5 + 3^5 + 5^5 + 7^5 + 17^5 + 23^5 + 40^5 = 5^5 + 10^5 + 16^5 + 16^5 + 19^5 + 20^5 + 40^5 = 1^5 + 8^5 + 14^5 + 16^5 + 21^5 + 27^5 + 39^5 = 7^5 + 8^5 + 11^5 + 14^5 + 16^5 + 33^5 + 37^5 = 4^5 + 7^5 + 8^5 + 13^5 + 26^5 + 31^5 + 37^5 = 1^5 + 5^5 + 6^5 + 20^5 + 28^5 + 29^5 + 37^5 = 3^5 + 3^5 + 7^5 + 18^5 + 27^5 + 32^5 + 36^5 = 6^5 + 12^5 + 18^5 + 25^5 + 30^5 + 31^5 + 34^5 = 6^5 + 10^5 + 20^5 + 27^5 + 27^5 + 33^5 + 33^5.
%H A346285 Sean A. Irvine, <a href="/A346285/b346285.txt">Table of n, a(n) for n = 1..10000</a>
%e A346285 36620574 is a term because 36620574 = 4^5 + 9^5 + 14^5 + 17^5 + 18^5 + 21^5 + 31^5 = 1^5 + 12^5 + 13^5 + 14^5 + 20^5 + 24^5 + 30^5 = 8^5 + 9^5 + 12^5 + 13^5 + 16^5 + 27^5 + 29^5 = 5^5 + 7^5 + 7^5 + 20^5 + 23^5 + 23^5 + 29^5 = 17^5 + 18^5 + 20^5 + 20^5 + 20^5 + 20^5 + 29^5 = 2^5 + 7^5 + 14^5 + 14^5 + 23^5 + 26^5 + 28^5 = 4^5 + 8^5 + 8^5 + 17^5 + 23^5 + 27^5 + 27^5 = 2^5 + 3^5 + 14^5 + 18^5 + 24^5 + 26^5 + 27^5.
%o A346285 (Python)
%o A346285 from itertools import combinations_with_replacement as cwr
%o A346285 from collections import defaultdict
%o A346285 keep = defaultdict(lambda: 0)
%o A346285 power_terms = [x**5 for x in range(1, 1000)]
%o A346285 for pos in cwr(power_terms, 7):
%o A346285     tot = sum(pos)
%o A346285     keep[tot] += 1
%o A346285     rets = sorted([k for k, v in keep.items() if v == 8])
%o A346285     for x in range(len(rets)):
%o A346285         print(rets[x])
%Y A346285 Cf. A345630, A345830, A346284, A346286, A346333, A346363.
%K A346285 nonn
%O A346285 1,1
%A A346285 _David Consiglio, Jr._, Jul 12 2021