A344364 Numbers that are the sum of three fourth powers in five or more ways.

292965218, 779888018, 1010431058, 1110995522, 1234349298, 1289202642, 1500533762, 1665914642, 1948502738, 2158376402, 2373191618, 2636686962, 2689817858, 2935465442, 3019732898, 3205282178, 3642994082, 3831800882, 4162186322, 4324686002, 4687443488, 5064808658

Offset: 1

Author

Sean A. Irvine, May 15 2021

Keywords

• nonn

Examples

			292965218 is a member of this sequence because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4 (actually has 6 representations, so is a member of this sequence but not of A344365).
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..10000

Crossrefs

Cf. A343967, A344277, A344356, A344365, A344647.

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])