A003340 Numbers that are the sum of 6 positive 4th powers.

6, 21, 36, 51, 66, 81, 86, 96, 101, 116, 131, 146, 161, 166, 181, 196, 211, 226, 246, 261, 276, 291, 306, 321, 326, 336, 341, 356, 371, 386, 401, 406, 421, 436, 451, 466, 486, 501, 516, 531, 546, 561, 576, 581, 596, 611, 626, 630, 641, 645, 660, 661, 675, 676, 690

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Eric Weisstein's World of Mathematics, Biquadratic Number.

Example

From David A. Corneth, Aug 04 2020: (Start)
13090 is in the sequence as 13090 = 4^4 + 4^4 + 5^4 + 6^4 + 8^4 + 9^4.
17539 is in the sequence as 17539 = 2^4 + 3^4 + 4^4 + 5^4 + 9^4 + 10^4.
23732 is in the sequence as 23732 = 3^4 + 5^4 + 5^4 + 7^4 + 10^4 + 10^4. (End)

Mathematica

Select[Range[1000], AnyTrue[PowersRepresentations[#, 6, 4], First[#]>0&]&] (* Jean-François Alcover, Jul 18 2017 *)

Prog

(Python)
from itertools import combinations_with_replacement as combs_with_rep
def aupto(limit):
    qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 5 <= limit]
    ss = set(sum(c) for c in combs_with_rep(qd, 6))
    return sorted(s for s in ss if s <= limit)
print(aupto(700)) # Michael S. Branicky, Jun 21 2021

Crossrefs

Cf. A000583, A003329, A003339, A003341, A003351, A345559, A345813.

Sequence in context: A063126 A256866 A115702 * A345813 A139606 A047717

Adjacent sequences: A003337 A003338 A003339 * A003341 A003342 A003343

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved