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A080686 Number of 19-smooth numbers <= n. 2

%I

%S 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,

%T 26,27,27,28,28,29,30,31,32,33,33,34,35,36,36,37,37,38,39,39,39,40,41,

%U 42,43,44,44,45,46,47,48,48,48,49,49,49,50,51,52,53,53,54,54,55,55,56

%N Number of 19-smooth numbers <= n.

%C 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.

%o (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","); ) }

%Y Cf. A071520, A051038.

%K easy,nonn

%O 1,2

%A _Cino Hilliard_, Mar 02 2003

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Last modified May 31 06:52 EDT 2020. Contains 334747 sequences. (Running on oeis4.)