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

1,1

Links

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

Example

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.

Prog

(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])

Crossrefs

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

Sequence in context: A235105 A205411 A219921 * A344353 A324898 A190933

Adjacent sequences: A344349 A344350 A344351 * A344353 A344354 A344355

Keyword

nonn

Author

David Consiglio, Jr., May 15 2021

Status

approved