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A346283 Numbers that are the sum of seven fifth powers in exactly six ways.

%I A346283 #6 Jul 31 2021 19:12:04
%S A346283 13562501,14583968,21555313,22057487,22066065,23089782,23345024,
%T A346283 24217918,24401574,24855016,24952718,24993517,25052501,25385064,
%U A346283 29558618,30653536,31613713,32559143,33005785,33533765,33635825,33828631,34267551,34268332,35431351,35736040
%N A346283 Numbers that are the sum of seven fifth powers in exactly six ways.
%C A346283 Differs from A345609 at term 15 because 28608832 = 3^5 + 4^5 + 4^5 + 8^5 + 10^5 + 24^5 + 29^5 = 2^5 + 12^5 + 12^5 + 16^5 + 18^5 + 24^5 + 28^5 = 6^5 + 6^5 + 14^5 + 14^5 + 22^5 + 22^5 + 28^5 = 7^5 + 8^5 + 13^5 + 14^5 + 17^5 + 26^5 + 27^5 = 2^5 + 8^5 + 11^5 + 19^5 + 22^5 + 23^5 + 27^5 = 6^5 + 6^5 + 12^5 + 14^5 + 24^5 + 24^5 + 26^5 = 7^5 + 7^5 + 8^5 + 16^5 + 24^5 + 25^5 + 25^5.
%H A346283 Sean A. Irvine, <a href="/A346283/b346283.txt">Table of n, a(n) for n = 1..10000</a>
%e A346283 13562501 is a term because 13562501 = 1^5 + 1^5 + 1^5 + 9^5 + 14^5 + 20^5 + 25^5 = 1^5 + 15^5 + 15^5 + 15^5 + 15^5 + 15^5 + 25^5 = 6^5 + 7^5 + 11^5 + 16^5 + 18^5 + 19^5 + 24^5 = 7^5 + 7^5 + 11^5 + 13^5 + 19^5 + 21^5 + 23^5 = 2^5 + 6^5 + 14^5 + 18^5 + 18^5 + 21^5 + 22^5 = 1^5 + 5^5 + 15^5 + 20^5 + 20^5 + 20^5 + 20^5.
%o A346283 (Python)
%o A346283 from itertools import combinations_with_replacement as cwr
%o A346283 from collections import defaultdict
%o A346283 keep = defaultdict(lambda: 0)
%o A346283 power_terms = [x**5 for x in range(1, 1000)]
%o A346283 for pos in cwr(power_terms, 7):
%o A346283     tot = sum(pos)
%o A346283     keep[tot] += 1
%o A346283     rets = sorted([k for k, v in keep.items() if v == 6])
%o A346283     for x in range(len(rets)):
%o A346283         print(rets[x])
%Y A346283 Cf. A345609, A345828, A346282, A346284, A346331, A346361.
%K A346283 nonn
%O A346283 1,1
%A A346283 _David Consiglio, Jr._, Jul 12 2021