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A345568 Numbers that are the sum of seven fourth powers in two or more ways.

%I A345568 #8 Jul 31 2021 17:57:50
%S A345568 262,277,292,307,342,357,372,422,437,502,517,532,547,597,612,677,772,
%T A345568 787,852,886,901,916,966,981,1027,1046,1141,1156,1221,1362,1377,1396,
%U A345568 1442,1510,1525,1557,1572,1587,1590,1617,1637,1652,1717,1765,1812,1827,1892
%N A345568 Numbers that are the sum of seven fourth powers in two or more ways.
%H A345568 Sean A. Irvine, <a href="/A345568/b345568.txt">Table of n, a(n) for n = 1..10000</a>
%e A345568 277 is a term because 277 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.
%o A345568 (Python)
%o A345568 from itertools import combinations_with_replacement as cwr
%o A345568 from collections import defaultdict
%o A345568 keep = defaultdict(lambda: 0)
%o A345568 power_terms = [x**4 for x in range(1, 1000)]
%o A345568 for pos in cwr(power_terms, 7):
%o A345568     tot = sum(pos)
%o A345568     keep[tot] += 1
%o A345568     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345568     for x in range(len(rets)):
%o A345568         print(rets[x])
%Y A345568 Cf. A003341, A345520, A345559, A345569, A345577, A345605, A345824.
%K A345568 nonn
%O A345568 1,1
%A A345568 _David Consiglio, Jr._, Jun 20 2021