cp's OEIS Frontend

A346335 Numbers that are the sum of eight fifth powers in exactly ten ways.

%I A346335 #6 Jul 31 2021 19:04:12
%S A346335 15539667,22932525,24393600,24650406,24952961,24953742,25142513,
%T A346335 26001294,27988486,28609075,29309819,31794336,32223105,32527286,
%U A346335 32610600,32807777,32890541,32998317,33015125,33187858,33361339,33550572,33659175,33782597,34029369,34073650
%N A346335 Numbers that are the sum of eight fifth powers in exactly ten ways.
%C A346335 Differs from A345618 at term 7 because 25054306 = 1^5 + 1^5 + 2^5 + 6^5 + 12^5 + 12^5 + 12^5 + 30^5 = 5^5 + 6^5 + 6^5 + 12^5 + 14^5 + 14^5 + 20^5 + 29^5 = 4^5 + 5^5 + 8^5 + 11^5 + 11^5 + 16^5 + 23^5 + 28^5 = 4^5 + 5^5 + 5^5 + 7^5 + 17^5 + 20^5 + 20^5 + 28^5 = 2^5 + 6^5 + 9^5 + 9^5 + 9^5 + 21^5 + 23^5 + 27^5 = 1^5 + 4^5 + 4^5 + 9^5 + 19^5 + 21^5 + 21^5 + 27^5 = 3^5 + 5^5 + 6^5 + 13^5 + 13^5 + 14^5 + 26^5 + 26^5 = 1^5 + 3^5 + 10^5 + 10^5 + 10^5 + 23^5 + 23^5 + 26^5 = 9^5 + 10^5 + 14^5 + 17^5 + 17^5 + 20^5 + 23^5 + 26^5 = 7^5 + 12^5 + 15^5 + 15^5 + 19^5 + 19^5 + 23^5 + 26^5 = 3^5 + 4^5 + 4^5 + 7^5 + 17^5 + 21^5 + 25^5 + 25^5.
%H A346335 Sean A. Irvine, <a href="/A346335/b346335.txt">Table of n, a(n) for n = 1..8261</a>
%e A346335 15539667 is a term because 15539667 = 1^5 + 7^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 27^5 = 1^5 + 4^5 + 7^5 + 9^5 + 13^5 + 13^5 + 13^5 + 27^5 = 1^5 + 1^5 + 7^5 + 7^5 + 10^5 + 16^5 + 19^5 + 26^5 = 1^5 + 1^5 + 2^5 + 10^5 + 12^5 + 17^5 + 18^5 + 26^5 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 16^5 + 23^5 + 24^5 = 4^5 + 11^5 + 13^5 + 13^5 + 15^5 + 15^5 + 22^5 + 24^5 = 5^5 + 6^5 + 13^5 + 15^5 + 15^5 + 19^5 + 20^5 + 24^5 = 3^5 + 10^5 + 12^5 + 12^5 + 18^5 + 18^5 + 20^5 + 24^5 = 6^5 + 9^5 + 11^5 + 11^5 + 15^5 + 21^5 + 22^5 + 22^5 = 3^5 + 5^5 + 10^5 + 19^5 + 19^5 + 20^5 + 20^5 + 21^5.
%o A346335 (Python)
%o A346335 from itertools import combinations_with_replacement as cwr
%o A346335 from collections import defaultdict
%o A346335 keep = defaultdict(lambda: 0)
%o A346335 power_terms = [x**5 for x in range(1, 1000)]
%o A346335 for pos in cwr(power_terms, 8):
%o A346335     tot = sum(pos)
%o A346335     keep[tot] += 1
%o A346335     rets = sorted([k for k, v in keep.items() if v == 10])
%o A346335     for x in range(len(rets)):
%o A346335         print(rets[x])
%Y A346335 Cf. A345618, A345842, A346259, A346334, A346345.
%K A346335 nonn
%O A346335 1,1
%A A346335 _David Consiglio, Jr._, Jul 13 2021