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A346331 Numbers that are the sum of eight fifth powers in exactly six ways.

%I A346331 #6 Jul 31 2021 19:03:56
%S A346331 1431397,2593811,3329119,3345410,3609912,3800722,3932480,4093604,
%T A346331 4096697,4114187,4129433,4154031,4169869,4377714,4451412,4475603,
%U A346331 4484634,4501409,4730845,4756642,4882770,4912477,4970823,5003645,5112274,5259111,5449985,5523925,5722189
%N A346331 Numbers that are the sum of eight fifth powers in exactly six ways.
%C A346331 Differs from A345614 at term 10 because 4104553 = 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 5^5 + 7^5 + 21^5 = 3^5 + 3^5 + 4^5 + 6^5 + 8^5 + 14^5 + 16^5 + 19^5 = 3^5 + 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 18^5 + 18^5 = 3^5 + 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 18^5 + 18^5 = 1^5 + 1^5 + 4^5 + 7^5 + 10^5 + 16^5 + 16^5 + 18^5 = 7^5 + 11^5 + 11^5 + 13^5 + 14^5 + 15^5 + 16^5 + 16^5 = 6^5 + 12^5 + 12^5 + 13^5 + 13^5 + 15^5 + 16^5 + 16^5.
%H A346331 Sean A. Irvine, <a href="/A346331/b346331.txt">Table of n, a(n) for n = 1..10000</a>
%e A346331 1431397 is a term because 1431397 = 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.
%o A346331 (Python)
%o A346331 from itertools import combinations_with_replacement as cwr
%o A346331 from collections import defaultdict
%o A346331 keep = defaultdict(lambda: 0)
%o A346331 power_terms = [x**5 for x in range(1, 1000)]
%o A346331 for pos in cwr(power_terms, 8):
%o A346331     tot = sum(pos)
%o A346331     keep[tot] += 1
%o A346331     rets = sorted([k for k, v in keep.items() if v == 6])
%o A346331     for x in range(len(rets)):
%o A346331         print(rets[x])
%Y A346331 Cf. A345614, A345838, A346283, A346330, A346332, A346341.
%K A346331 nonn
%O A346331 1,1
%A A346331 _David Consiglio, Jr._, Jul 13 2021