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A344353 Numbers that are the sum of four fourth powers in exactly four ways. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A344352 at term 52 because 2147874 = 2^4 + 14^4 + 31^4 + 33^4 = 4^4 + 23^4 + 27^4 + 34^4 = 7^4 + 21^4 + 28^4 + 34^4 = 12^4 + 17^4 + 29^4 + 34^4 = 14^4 + 18^4 + 19^4 + 37^4.

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. A343972, A344242, A344278, A344352, A344355, A344357.

Sequence in context: A205411 A219921 A344352 * A324898 A190933 A122474

Adjacent sequences:  A344350 A344351 A344352 * A344354 A344355 A344356

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., May 15 2021

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)