OFFSET
1,2
COMMENTS
Range = primes 2 to 17. Input pn=17 in script below. Code below is much faster than the code for cross-reference. For input of n=200 13 times as fast and many times faster for larger input of n.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
Accumulate[Table[Boole[Max[FactorInteger[n][[;; , 1]]] <= 17], {n, 100}]] (* Amiram Eldar, Apr 29 2025 *)
PROG
(PARI) smoothn(n, pn) = { for(m=1, n, pr=1; forprime(p=2, pn, pr*=p; ); ct=1; for(x=1, m, f=0; forprime(y=nextprime(pn+1), floor(x), if(x%y == 0, f=1; break) ); if(gcd(x, pr)<>1, if(f==0, ct+=1; )) ); print1(ct", "); ) }
(Python)
from sympy import integer_log
def A080685(n):
ptuple = (2, 3, 5, 7, 11, 13, 17)
def g(x, m): return sum(g(x//(ptuple[m]**i), m-1)for i in range(integer_log(x, ptuple[m])[0]+1)) if m else x.bit_length()
return g(n, 6) # Chai Wah Wu, Mar 15 2026
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Mar 02 2003
STATUS
approved