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A345823 Numbers that are the sum of seven fourth powers in exactly one ways.

%I A345823 #6 Jul 31 2021 21:36:35
%S A345823 7,22,37,52,67,82,87,97,102,112,117,132,147,162,167,177,182,197,212,
%T A345823 227,242,247,322,327,337,352,387,402,407,417,452,467,482,487,562,567,
%U A345823 577,582,592,627,631,642,646,657,661,662,676,691,692,706,707,711,721,722
%N A345823 Numbers that are the sum of seven fourth powers in exactly one ways.
%C A345823 Differs from A003341 at term 23 because 262 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.
%H A345823 Sean A. Irvine, <a href="/A345823/b345823.txt">Table of n, a(n) for n = 1..10000</a>
%e A345823 22 is a term because 22 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.
%o A345823 (Python)
%o A345823 from itertools import combinations_with_replacement as cwr
%o A345823 from collections import defaultdict
%o A345823 keep = defaultdict(lambda: 0)
%o A345823 power_terms = [x**4 for x in range(1, 1000)]
%o A345823 for pos in cwr(power_terms, 7):
%o A345823     tot = sum(pos)
%o A345823     keep[tot] += 1
%o A345823     rets = sorted([k for k, v in keep.items() if v == 1])
%o A345823     for x in range(len(rets)):
%o A345823         print(rets[x])
%Y A345823 Cf. A003341, A345773, A345813, A345824, A345833, A346278.
%K A345823 nonn
%O A345823 1,1
%A A345823 _David Consiglio, Jr._, Jun 26 2021