A047716 Sums of 5 but no fewer nonzero fourth 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, 629, 644, 659, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 1..16998 (terms <= 200000)

Crossrefs

Subsequence of A003339.

Cf. A000583, A002377, A344187, A344188, A344189.

Programs

PARI

upto(n)={my(e=5); my(s=sum(k=1, sqrtint(sqrtint(n)), x^(k^4)) + O(x*x^n)); my(p=s^e, q=(1 + s)^(e-1)); select(k->polcoeff(p,k) && !polcoeff(q,k), [1..n])} \\ Andrew Howroyd, Jul 06 2018

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, k)) for k in range(6)]
  return sorted(filter(lambda x: x <= limit, ss[5]-ss[4]-ss[3]-ss[2]-ss[1]))
print(aupto(800)) # Michael S. Branicky, May 20 2021

Formula

Equals A003339 - A344189 - A344188 - A344187 - A000583. - Sean A. Irvine, May 15 2021