A047718 Numbers that are the sum of 7 but no fewer nonzero fourth powers.

7, 22, 37, 52, 67, 87, 102, 112, 117, 132, 147, 167, 177, 182, 197, 212, 227, 242, 247, 262, 277, 292, 307, 322, 327, 342, 352, 357, 372, 387, 402, 407, 417, 422, 437, 452, 467, 482, 487, 502, 517, 532, 547, 562, 567, 577, 582, 592, 597, 612, 631, 646, 662

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 1..26439 (terms <= 200000)

Crossrefs

Cf. A000583, A002377, A003341.

Programs

PARI

upto(n)={my(e=7); 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 mc
def aupto(limit):
    qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 6 <= limit]
    ss = [set(sum(c) for c in mc(qd, i)) for i in range(8)]
    s7nf = ss[7] - ss[6] - ss[5] - ss[4] - ss[3] - ss[2] - ss[1]
    return sorted(s for s in s7nf if s <= limit)
print(aupto(663)) # Michael S. Branicky, Jul 22 2021