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%I #6 Jul 31 2021 17:25:47
%S 1620,2660,2725,2740,2835,2855,2870,2900,2915,2920,2935,2950,2965,
%T 2980,3000,3015,3030,3045,3095,3110,3160,3175,3190,3205,3220,3240,
%U 3255,3270,3285,3335,3350,3415,3430,3445,3460,3479,3510,3525,3544,3559,3574,3589,3639
%N Numbers that are the sum of ten fourth powers in four or more ways.
%H Sean A. Irvine, <a href="/A345597/b345597.txt">Table of n, a(n) for n = 1..10000</a>
%e 2660 is a term because 2660 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4.
%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, 10):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 4])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345552, A345588, A345596, A345598, A345636, A345856.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 20 2021
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