A344352 Numbers that are the sum of four fourth powers in four or more ways.

236674, 282018, 300834, 334818, 478338, 637794, 650034, 650658, 708483, 708834, 729938, 789378, 816578, 832274, 849954, 941859, 989043, 1042083, 1045539, 1099203, 1099458, 1102258, 1179378, 1243074, 1257954, 1283874, 1323234, 1334979, 1339074, 1342979, 1352898, 1357059, 1379043, 1518578

Offset: 1

Author

David Consiglio, Jr., May 15 2021

Keywords

• nonn

Examples

			300834 is a term of this sequence because 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.
		

Links

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

Crossrefs

Cf. A343971, A344241, A344277, A344353, A344354, A344356.

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(1,200)]
count = 1
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
    count += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
    print(rets[x])