A003339 Numbers that are the sum of 5 positive 4th powers.

5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 260, 275, 290, 305, 320, 325, 340, 355, 370, 385, 405, 420, 435, 450, 500, 515, 530, 545, 560, 580, 595, 610, 625, 629, 644, 659, 674, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			From _David A. Corneth_, Aug 04 2020: (Start)
22418 is in the sequence as 22418 = 1^4 + 2^4 + 7^4 + 10^4 + 10^4.
30004 is in the sequence as 30004 = 2^4 + 3^4 + 5^4 + 11^4 + 11^4.
39028 is in the sequence as 39028 = 5^4 + 5^4 + 7^4 + 11^4 + 12^4. (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

Supersequence of A047716.

Cf. A000583, A003328, A003338, A003340, A003350, A344190, A344238.

Programs

Mathematica

Select[Range[1000], AnyTrue[PowersRepresentations[#, 5, 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 + 4 <= limit]
  ss = set(sum(c) for c in combs_with_rep(qd, 5))
  return sorted(s for s in ss if s <= limit)
print(aupto(800)) # Michael S. Branicky, May 20 2021