A247509 Number of preprimes (A156759, n>1) such that the smallest prime divisor equals prime(n).

3, 3, 2, 4, 2, 3, 2, 2, 3, 2, 4, 3, 2, 2, 3, 3, 2, 4, 3, 2, 3, 2, 2, 4, 3, 2, 3, 2, 2, 5, 2, 3, 2, 4, 2, 3, 3, 2, 3, 3, 2, 5, 2, 3, 2, 3, 5, 3, 2, 2, 3, 2, 3, 3, 3, 3, 2, 4, 3, 2, 2, 5, 3, 2, 2, 3, 2, 4, 2, 2, 2, 3, 3, 3, 2, 2, 3, 2, 2, 3, 2, 4, 2, 3, 2, 2, 4

Offset: 1

Author

Vladimir Shevelev, Sep 18 2014

Keywords

• nonn

Examples

			For n=2, using the formula, we have a(2)=pi(25/3)-1=3.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..1000
• Vladimir Shevelev, A classification of the positive integers over primes

Crossrefs

Cf. A000040, A156759, A247393, A247394.

Programs

Mathematica

a[1] = 3;a[n_] := PrimePi[Prime[n + 1]^2 / Prime[n]] - n + 1; Table[a[n], {n, 1, 87}] (* Indranil Ghosh, Mar 09 2017 *)

PARI

for (n=1, 87, print1(if(n==1, 3, primepi(prime(n + 1)^2 / prime(n)) - n + 1),", ")) \\ Indranil Ghosh, Mar 09 2017

Formula

For n>1, a(n) = pi(prime(n+1)^2/prime(n))-n +1, where pi(x) is the prime counting function (cf. A000720). - Vladimir Shevelev, Sep 28 2014

Extensions

More terms from Peter J. C. Moses, Sep 18 2014