A344365 Numbers that are the sum of three fourth powers in exactly five ways.

1234349298, 1289202642, 1948502738, 2935465442, 4162186322, 5632212978, 7360969778, 8657437698, 8753497298, 11079947522, 15784025138, 17536524642, 19749588768, 20627242272, 21318234098, 31176043808, 35240346162, 37459676898, 39912730578, 42901649042

Offset: 1

Author

Sean A. Irvine, May 15 2021

Keywords

• nonn

Examples

			1234349298 is a member of this sequence because 1234349298 = 7^4 + 154^4 + 161^4 = 26^4 + 143^4 + 169^4 = 61^4 + 118^4 + 179^4 = 74^4 + 107^4 + 181^4 = 91^4 + 91^4 + 182^4.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..946

Crossrefs

Cf. A343970, A344278, A344357, A344364, A344648.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 500)]
for pos in cwr(power_terms, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 5])
for x in range(len(rets)):
    print(rets[x])