A345574 - OEIS

%I #6 Jul 31 2021 17:58:11

%S 19491,21252,21267,21332,21507,21636,21876,23652,25347,30372,31251,

%T 31412,31652,32116,32356,33811,33907,35427,35637,35652,35892,36052,

%U 36261,37812,37827,38052,38067,38596,38676,39267,39347,39891,39971,39972,40212,40356,40452

%N Numbers that are the sum of seven fourth powers in eight or more ways.

%H Sean A. Irvine, <a href="/A345574/b345574.txt">Table of n, a(n) for n = 1..10000</a>

%e 21252 is a term because 21252 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 12^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 11^4 = 1^4 + 1^4 + 7^4 + 8^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 11^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 12^4 = 1^4 + 2^4 + 4^4 + 6^4 + 9^4 + 9^4 + 9^4 = 1^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 11^4 = 3^4 + 4^4 + 6^4 + 7^4 + 8^4 + 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 >= 8])

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

%o         print(rets[x])

%Y Cf. A345526, A345565, A345573, A345575, A345583, A345630, A345830.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021