A247977 If n = 1 or prime, then a(n) = 0; otherwise, if n is a preprime of k-th kind, then a(n) = k.

0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 3, 2, 3, 0, 3, 0, 3, 2, 3, 1, 3, 0, 3, 2, 3, 0, 3, 0, 3, 2, 3, 0, 3, 1, 4, 3, 4, 0, 4, 2, 4, 3, 4, 0, 4, 0, 4, 3, 4, 2, 4, 0, 4, 3, 4, 0, 4, 0, 4, 3, 4, 1, 4, 0, 4, 3, 4, 0, 4, 2, 4, 3, 4, 0, 4, 1, 4, 3, 4, 2, 4, 0, 4, 3, 4, 0, 4, 0, 4, 3, 4, 0, 4, 0, 4, 3, 4, 0, 4, 2, 4, 3, 4, 1, 4, 1, 5, 4, 5, 3

Offset

1,10

Comments

Preprimes of k-th kind are defined in comment in A247395.

Links

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Vladimir Shevelev , A classification of the positive integers over primes

Formula

If n is a composite number, then a(n) = pi(sqrt(n)) - pi(lpf(n)) + 1, where pi(x) is prime counting function (cf. A000720), lpf = least prime factor (A020639).

Example

If n = 15, then, by the formula, we have a(15) = 2 - 2 + 1 = 1.

Mathematica

Table[If[n==1 || PrimeQ[n], 0, PrimePi[Sqrt[n]] - PrimePi[FactorInteger[n][[1, 1]]] + 1], {n, 1, 125}] (* Indranil Ghosh, Mar 08 2017 *)

Prog

(PARI) for(n=1, 125, print1(if(n==1 || isprime(n), 0, primepi(sqrt(n)) - primepi(vecmin(factor(n)[, 1])) + 1), ", ")) \\ Indranil Ghosh, Mar 08 2017

Crossrefs

Cf. A000040, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247834, A247835.

Sequence in context: A339927 A227957 A305575 * A359239 A143232 A329981

Adjacent sequences: A247974 A247975 A247976 * A247978 A247979 A247980

Keyword

nonn,look

Author

Vladimir Shevelev, Sep 28 2014

Status

approved