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Numbers that are the sum of nine fourth powers in exactly one ways.
7

%I #6 Jul 31 2021 21:28:12

%S 9,24,39,54,69,84,89,99,104,114,119,129,134,144,149,164,169,179,184,

%T 194,199,209,214,229,244,249,259,274,329,354,369,384,409,419,434,449,

%U 484,489,499,514,569,594,609,624,633,648,649,659,663,674,678,689,693,708

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

%C 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 Sean A. Irvine, <a href="/A345843/b345843.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 9):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 1])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A003343, A345793, A345833, A345844, A345853, A346336.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021