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A345813 Numbers that are the sum of six fourth powers in exactly one ways.

%I A345813 #6 Jul 31 2021 21:57:09
%S A345813 6,21,36,51,66,81,86,96,101,116,131,146,161,166,181,196,211,226,246,
%T A345813 306,321,326,336,371,386,401,406,436,451,466,486,501,546,561,576,581,
%U A345813 611,626,630,641,645,660,661,675,676,690,691,705,706,710,725,740,755,756
%N A345813 Numbers that are the sum of six fourth powers in exactly one ways.
%C A345813 Differs from A003340 at term 20 because 261 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4.
%H A345813 Sean A. Irvine, <a href="/A345813/b345813.txt">Table of n, a(n) for n = 1..10000</a>
%e A345813 21 is a term because 21 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.
%o A345813 (Python)
%o A345813 from itertools import combinations_with_replacement as cwr
%o A345813 from collections import defaultdict
%o A345813 keep = defaultdict(lambda: 0)
%o A345813 power_terms = [x**4 for x in range(1, 1000)]
%o A345813 for pos in cwr(power_terms, 6):
%o A345813     tot = sum(pos)
%o A345813     keep[tot] += 1
%o A345813     rets = sorted([k for k, v in keep.items() if v == 1])
%o A345813     for x in range(len(rets)):
%o A345813         print(rets[x])
%Y A345813 Cf. A003340, A048929, A344190, A345814, A345823, A346356.
%K A345813 nonn
%O A345813 1,1
%A A345813 _David Consiglio, Jr._, Jun 26 2021