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A047716 Sums of 5 but no fewer nonzero fourth powers. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

PROG

(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

CROSSREFS

Subsequence of A003339.

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

Sequence in context: A029528 A101867 A003339 * A344190 A326005 A063110

Adjacent sequences:  A047713 A047714 A047715 * A047717 A047718 A047719

KEYWORD

nonn

AUTHOR

Arlin Anderson (starship1(AT)gmail.com)

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)