A345813 Numbers that are the sum of six fourth powers in exactly one ways.

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

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