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A344923 Numbers that are the sum of four fourth powers in exactly seven ways.

%I A344923 #6 Jul 31 2021 22:12:16
%S A344923 6576339,16020018,16408434,22673634,23056803,33734834,39786098,
%T A344923 43583138,51071619,52652754,53731458,57976083,63985314,64365939,
%U A344923 67655779,68846274,73744563,75951138,77495778,87038883,88648914,89148114,90665058,90818898,92800178,93830803
%N A344923 Numbers that are the sum of four fourth powers in exactly seven ways.
%C A344923 Differs from A344922 at term 2 because 13155858 = 1^4 + 16^4 + 19^4 + 60^4  = 3^4 + 6^4 + 21^4 + 60^4  = 10^4 + 18^4 + 31^4 + 59^4  = 12^4 + 27^4 + 45^4 + 54^4  = 15^4 + 44^4 + 46^4 + 47^4  = 18^4 + 25^4 + 41^4 + 56^4  = 29^4 + 30^4 + 44^4 + 53^4  = 35^4 + 36^4 + 38^4 + 53^4.
%H A344923 David Consiglio, Jr., <a href="/A344923/b344923.txt">Table of n, a(n) for n = 1..100</a>
%e A344923 6576339 is a term because 6576339 = 1^4 + 24^4 + 41^4 + 43^4  = 3^4 + 7^4 + 41^4 + 44^4  = 4^4 + 23^4 + 27^4 + 49^4  = 6^4 + 31^4 + 41^4 + 41^4  = 7^4 + 11^4 + 36^4 + 47^4  = 7^4 + 21^4 + 28^4 + 49^4  = 12^4 + 17^4 + 29^4 + 49^4.
%o A344923 (Python)
%o A344923 from itertools import combinations_with_replacement as cwr
%o A344923 from collections import defaultdict
%o A344923 keep = defaultdict(lambda: 0)
%o A344923 power_terms = [x**4 for x in range(1, 1000)]
%o A344923 for pos in cwr(power_terms, 4):
%o A344923     tot = sum(pos)
%o A344923     keep[tot] += 1
%o A344923 rets = sorted([k for k, v in keep.items() if v == 7])
%o A344923 for x in range(len(rets)):
%o A344923     print(rets[x])
%Y A344923 Cf. A344730, A344921, A344922, A344925, A344943, A345151.
%K A344923 nonn
%O A344923 1,1
%A A344923 _David Consiglio, Jr._, Jun 02 2021