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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			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)
		

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.

Crossrefs

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

Programs

Mathematica

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

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