A344357 - OEIS

%I #12 Jul 31 2021 22:12:09

%S 2147874,2266338,2690658,3189603,3464178,3754674,4030419,4165794,

%T 4457298,4884114,5229378,5978883,5980178,5981283,6014178,6134994,

%U 6258723,6313953,6400194,6612354,7088898,7498323,7811874,7918498,8064018,8292323,8630259,9146034,9269523,9388978,9397683,9726978

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

%C Differs from A344356 at term 7 because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.

%H David Consiglio, Jr., <a href="/A344357/b344357.txt">Table of n, a(n) for n = 1..20000</a>

%e 2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.

%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, 4):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 5])

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

%o     print(rets[x])

%Y Cf. A343986, A344353, A344356, A344359, A344365, A344921.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 15 2021