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A344239 Numbers that are the sum of three fourth powers in three or more ways.

%I A344239 #12 May 10 2024 02:20:20
%S A344239 811538,1733522,2798978,3750578,4614722,5978882,6573938,7303842,
%T A344239 8878898,12771458,12984608,13760258,14677362,15601698,15916082,
%U A344239 16196193,17868242,20621042,21556178,22349522,22673378,25190802,25589858,27736352,29969282,30623138,33998258,39765362,41532498,44048498
%N A344239 Numbers that are the sum of three fourth powers in three or more ways.
%H A344239 David Consiglio, Jr., <a href="/A344239/b344239.txt">Table of n, a(n) for n = 1..14213</a>
%e A344239 2798978 =  6^4 + 31^4 + 37^4
%e A344239         =  9^4 + 29^4 + 38^4
%e A344239         = 13^4 + 26^4 + 39^4
%e A344239 so 2798978 is a term of this sequence.
%o A344239 (Python)
%o A344239 from itertools import combinations_with_replacement as cwr
%o A344239 from collections import defaultdict
%o A344239 keep = defaultdict(lambda: 0)
%o A344239 power_terms = [x**4 for x in range(1,50)]
%o A344239 for pos in cwr(power_terms,3):
%o A344239     tot = sum(pos)
%o A344239     keep[tot] += 1
%o A344239 rets = sorted([k for k,v in keep.items() if v >= 3])
%o A344239 for x in range(len(rets)):
%o A344239     print(rets[x])
%Y A344239 Cf. A025398, A309762, A344240, A344241, A344277.
%K A344239 nonn
%O A344239 1,1
%A A344239 _David Consiglio, Jr._, May 12 2021