A080686 Number of 19-smooth numbers <= n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 32, 33, 33, 34, 35, 36, 36, 37, 37, 38, 39, 39, 39, 40, 41, 42, 43, 44, 44, 45, 46, 47, 48, 48, 48, 49, 49, 49, 50, 51, 52, 53, 53, 54, 54, 55, 55, 56

Offset

1,2

Comments

Range = primes 2 to 19. Input pn=19 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

Table of n, a(n) for n=1..72.

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, prevprime
def A080686(n):
    def g(x, m): return sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1)) if m==3 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
    return g(n, 19) # Chai Wah Wu, Sep 17 2024

Crossrefs

Cf. A071520, A051038.

Sequence in context: A296089 A323368 A369259 * A036218 A172275 A025484

Adjacent sequences: A080683 A080684 A080685 * A080687 A080688 A080689

Keyword

easy,nonn

Author

Cino Hilliard, Mar 02 2003

Status

approved