A344244 Numbers that are the sum of five fourth powers in exactly three ways.

4225, 6610, 6850, 9170, 9235, 9490, 11299, 12929, 14209, 14690, 14755, 14770, 15314, 16579, 16594, 16659, 16834, 17203, 17235, 17315, 17859, 17874, 17939, 18785, 18850, 18979, 19154, 19700, 19715, 20674, 21250, 21330, 21364, 21410, 21954, 23139, 23795, 24754, 25810, 26578, 28610, 28930, 29330, 29699

Offset: 1

Author

David Consiglio, Jr., May 12 2021

Keywords

• nonn

Comments

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

Examples

			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
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Crossrefs

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

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(1,50)]
for pos in cwr(power_terms,5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 3])
for x in range(len(rets)):
    print(rets[x])