A345828 - OEIS

%I #6 Jul 31 2021 21:36:53

%S 10787,15396,15411,15586,15651,16611,16626,16676,16866,17956,18867,

%T 19156,19236,19251,19411,19426,19666,20035,20771,21012,21187,21397,

%U 21412,21442,21492,21572,21621,21811,21891,22116,22132,22292,22307,22372,22595,22660,22962

%N Numbers that are the sum of seven fourth powers in exactly six ways.

%C Differs from A345572 at term 9 because 16691 = 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4  = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4  = 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4  = 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4  = 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4  = 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4  = 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.

%H Sean A. Irvine, <a href="/A345828/b345828.txt">Table of n, a(n) for n = 1..10000</a>

%e 15396 is a term because 15396 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 11^4 = 1^4 + 3^4 + 4^4 + 4^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 9^4 + 9^4.

%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, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 6])

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

%o         print(rets[x])

%Y Cf. A345572, A345778, A345818, A345827, A345829, A345838, A346283.

%K nonn

%O 1,1

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