A047721 Sum of 10 but no fewer nonzero fourth powers.

10, 25, 40, 55, 70, 90, 105, 120, 135, 150, 160, 170, 185, 200, 215, 225, 230, 250, 265, 280, 295, 310, 330, 345, 360, 375, 390, 400, 410, 425, 440, 455, 465, 470, 485, 490, 505, 520, 535, 550, 565, 570, 585, 600, 615, 634, 640, 650, 665, 680, 695, 714, 730

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 1..15256

Crossrefs

Cf. A000583, A002377, A003344, A047720, A047722, A047723.

Programs

PARI

upto(n)={my(e=10); 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 count, takewhile, combinations_with_replacement as mc
def aupto(lim):
    p4 = list(takewhile(lambda x: x <= lim, (i**4 for i in count(1))))
    s = [set(sum(c) for c in mc(p4, i) if sum(c) <= lim) for i in range(11)]
    ans = s[10]
    for i in range(1, 10):
        ans -= s[i]
    return sorted(ans)
print(aupto(730)) # Michael S. Branicky, Oct 25 2021