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A047718
Numbers that are the sum of 7 but no fewer nonzero fourth powers.
2
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
1,1
LINKS
David A. Corneth, Table of n, a(n) for n = 1..26439 (terms <= 200000)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved