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

1,1

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Vladimir Shevelev, A classification of the positive integers over primes

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A156759, A247393, A247394.

Sequence in context: A064655 A207335 A049604 * A106686 A106702 A303338

Adjacent sequences: A247506 A247507 A247508 * A247510 A247511 A247512

Keyword

nonn

Author

Vladimir Shevelev, Sep 18 2014

Extensions

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

Status

approved