A344244 - OEIS

%I #7 Jul 31 2021 22:02:52

%S 4225,6610,6850,9170,9235,9490,11299,12929,14209,14690,14755,14770,

%T 15314,16579,16594,16659,16834,17203,17235,17315,17859,17874,17939,

%U 18785,18850,18979,19154,19700,19715,20674,21250,21330,21364,21410,21954,23139,23795,24754,25810,26578,28610,28930,29330,29699

%N Numbers that are the sum of five fourth powers in exactly three ways.

%C Differs from A344243 at term 31 because 20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4 = 2^4 + 3^4 + 3^4 + 3^4 + 12^4 = 2^4 + 6^4 + 9^4 + 9^4 + 9^4 = 4^4 + 6^4 + 7^4 + 7^4 + 11^4

%H David Consiglio, Jr., <a href="/A344244/b344244.txt">Table of n, a(n) for n = 1..20000</a>

%e 6850 is a member of this sequence because 6850 =  = 1^4 + 2^4 + 2^4 + 4^4 + 9^4 = 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 3^4 + 3^4 + 6^4 + 6^4 + 8^4

%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(1,50)]

%o for pos in cwr(power_terms,5):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k,v in keep.items() if v == 3])

%o for x in range(len(rets)):

%o     print(rets[x])

%Y Cf. A342688, A343705, A344237, A344242, A344243, A344355, A345815.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 12 2021