A345845 - OEIS

%I #6 Jul 31 2021 21:28:19

%S 519,534,599,774,1143,1364,1539,1604,1619,1814,2579,2644,2659,2679,

%T 2694,2709,2724,2739,2754,2759,2774,2789,2819,2834,2839,2869,2884,

%U 2899,2994,2999,3079,3109,3124,3139,3303,3318,3333,3334,3363,3364,3379,3383,3398,3463

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

%C Differs from A345587 at term 26 because 285.

%H Sean A. Irvine, <a href="/A345845/b345845.txt">Table of n, a(n) for n = 1..10000</a>

%e 534 is a term because 534 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

%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 == 3])

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

%o         print(rets[x])

%Y Cf. A345587, A345795, A345835, A345844, A345846, A345855, A346338.

%K nonn

%O 1,1

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