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A345843 Numbers that are the sum of nine fourth powers in exactly one ways.

%I A345843 #6 Jul 31 2021 21:28:12
%S A345843 9,24,39,54,69,84,89,99,104,114,119,129,134,144,149,164,169,179,184,
%T A345843 194,199,209,214,229,244,249,259,274,329,354,369,384,409,419,434,449,
%U A345843 484,489,499,514,569,594,609,624,633,648,649,659,663,674,678,689,693,708
%N A345843 Numbers that are the sum of nine fourth powers in exactly one ways.
%C A345843 Differs from A003343 at term 28 because 264 = 1^4 + 1^4 + 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 + 1^4 + 1^4 + 4^4.
%H A345843 Sean A. Irvine, <a href="/A345843/b345843.txt">Table of n, a(n) for n = 1..10000</a>
%e A345843 24 is a term because 24 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.
%o A345843 (Python)
%o A345843 from itertools import combinations_with_replacement as cwr
%o A345843 from collections import defaultdict
%o A345843 keep = defaultdict(lambda: 0)
%o A345843 power_terms = [x**4 for x in range(1, 1000)]
%o A345843 for pos in cwr(power_terms, 9):
%o A345843     tot = sum(pos)
%o A345843     keep[tot] += 1
%o A345843     rets = sorted([k for k, v in keep.items() if v == 1])
%o A345843     for x in range(len(rets)):
%o A345843         print(rets[x])
%Y A345843 Cf. A003343, A345793, A345833, A345844, A345853, A346336.
%K A345843 nonn
%O A345843 1,1
%A A345843 _David Consiglio, Jr._, Jun 26 2021