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A344941 Numbers that are the sum of five fourth powers in exactly six ways. 7
151300, 225890, 236194, 243235, 246674, 250834, 286114, 288579, 300835, 302130, 302210, 303235, 309059, 317795, 320195, 334819, 334899, 335443, 336210, 338914, 346835, 356899, 363379, 366995, 373234, 375619, 389875, 391154, 392259, 393314, 394354, 412339 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A344940 at term 2 because 197779 = 1^4 + 5^4 + 6^4 + 16^4 + 19^4  = 1^4 + 7^4 + 11^4 + 12^4 + 20^4  = 1^4 + 10^4 + 12^4 + 17^4 + 17^4  = 2^4 + 4^4 + 5^4 + 7^4 + 21^4  = 3^4 + 5^4 + 6^4 + 6^4 + 21^4  = 4^4 + 7^4 + 9^4 + 13^4 + 20^4  = 11^4 + 13^4 + 14^4 + 15^4 + 16^4.

LINKS

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

EXAMPLE

151300 is a term because 151300 = 3^4 + 3^4 + 3^4 + 12^4 + 19^4  = 3^4 + 11^4 + 11^4 + 14^4 + 17^4  = 3^4 + 13^4 + 13^4 + 13^4 + 16^4  = 6^4 + 9^4 + 9^4 + 9^4 + 19^4  = 7^4 + 11^4 + 11^4 + 11^4 + 18^4  = 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

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, 1000)]

for pos in cwr(power_terms, 5):

    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. A344359, A344921, A344940, A344943, A345175, A345818.

Sequence in context: A343679 A246285 A344940 * A334005 A251987 A205662

Adjacent sequences:  A344938 A344939 A344940 * A344942 A344943 A344944

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 03 2021

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)