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A345813 Numbers that are the sum of six fourth powers in exactly one ways. 6
6, 21, 36, 51, 66, 81, 86, 96, 101, 116, 131, 146, 161, 166, 181, 196, 211, 226, 246, 306, 321, 326, 336, 371, 386, 401, 406, 436, 451, 466, 486, 501, 546, 561, 576, 581, 611, 626, 630, 641, 645, 660, 661, 675, 676, 690, 691, 705, 706, 710, 725, 740, 755, 756 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Differs from A003340 at term 20 because 261 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4.

LINKS

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

EXAMPLE

21 is a term because 21 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

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, 6):

    tot = sum(pos)

    keep[tot] += 1

    rets = sorted([k for k, v in keep.items() if v == 1])

    for x in range(len(rets)):

        print(rets[x])

CROSSREFS

Cf. A003340, A048929, A344190, A345814, A345823, A346356.

Sequence in context: A256866 A115702 A003340 * A139606 A047717 A089982

Adjacent sequences:  A345810 A345811 A345812 * A345814 A345815 A345816

KEYWORD

nonn

AUTHOR

David Consiglio, Jr., Jun 26 2021

STATUS

approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)