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A345824 Numbers that are the sum of seven fourth powers in exactly two ways.

%I A345824 #6 Jul 31 2021 21:36:39
%S A345824 262,277,292,307,342,357,372,422,437,502,517,532,547,597,612,677,772,
%T A345824 787,852,886,901,916,966,981,1027,1046,1141,1156,1221,1362,1377,1396,
%U A345824 1442,1510,1525,1557,1572,1587,1590,1617,1637,1652,1717,1765,1812,1827,1892
%N A345824 Numbers that are the sum of seven fourth powers in exactly two ways.
%C A345824 Differs from A345568 at term 61.
%H A345824 Sean A. Irvine, <a href="/A345824/b345824.txt">Table of n, a(n) for n = 1..10000</a>
%e A345824 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 A345824 (Python)
%o A345824 from itertools import combinations_with_replacement as cwr
%o A345824 from collections import defaultdict
%o A345824 keep = defaultdict(lambda: 0)
%o A345824 power_terms = [x**4 for x in range(1, 1000)]
%o A345824 for pos in cwr(power_terms, 7):
%o A345824     tot = sum(pos)
%o A345824     keep[tot] += 1
%o A345824     rets = sorted([k for k, v in keep.items() if v == 2])
%o A345824     for x in range(len(rets)):
%o A345824         print(rets[x])
%Y A345824 Cf. A345568, A345774, A345814, A345823, A345825, A345834, A346279.
%K A345824 nonn
%O A345824 1,1
%A A345824 _David Consiglio, Jr._, Jun 26 2021