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A344648 Numbers that are the sum of three fourth powers in exactly six ways. 6
292965218, 1010431058, 1110995522, 1500533762, 1665914642, 2158376402, 2373191618, 2636686962, 2689817858, 3019732898, 3205282178, 3642994082, 3831800882, 4324686002, 4687443488, 5064808658, 5175310322, 6317554418, 6450435362, 6720346178, 7018992162, 7635761042, 7781780258 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A344647 at term 2 because 779888018 = 3^4 + 139^4 + 142^4 = 9^4 + 38^4 + 167^4 = 14^4 + 133^4 + 147^4 = 43^4 + 114^4 + 157^4 = 47^4 + 111^4 + 158^4 = 63^4 + 98^4 + 161^4 = 73^4 + 89^4 + 162^4.

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..5000

EXAMPLE

1010431058 is a term because 1010431058 = 13^4 + 143^4 + 156^4 = 31^4 + 132^4 + 163^4 = 44^4 + 123^4 + 167^4 = 52^4 + 117^4 + 169^4 = 69^4 + 103^4 + 172^4 = 81^4 + 92^4 + 173^4.

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 == 6])

for x in range(len(rets)):

    print(rets[x])

CROSSREFS

Cf. A344365, A344647, A344730, A344921, A345084.

Sequence in context: A204055 A344364 A344647 * A251566 A112452 A291459

Adjacent sequences:  A344645 A344646 A344647 * A344649 A344650 A344651

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., May 25 2021

STATUS

approved

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Last modified August 18 13:09 EDT 2022. Contains 356212 sequences. (Running on oeis4.)