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A344364 Numbers that are the sum of three fourth powers in five or more ways. 6
292965218, 779888018, 1010431058, 1110995522, 1234349298, 1289202642, 1500533762, 1665914642, 1948502738, 2158376402, 2373191618, 2636686962, 2689817858, 2935465442, 3019732898, 3205282178, 3642994082, 3831800882, 4162186322, 4324686002, 4687443488, 5064808658 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..10000

EXAMPLE

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.

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, 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])

CROSSREFS

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

Sequence in context: A183737 A234807 A204055 * A344647 A344648 A251566

Adjacent sequences:  A344361 A344362 A344363 * A344365 A344366 A344367

KEYWORD

nonn

AUTHOR

Sean A. Irvine, May 15 2021

STATUS

approved

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Last modified August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)