A156759 -id:A156759 - cp's OEIS frontend

A247835 Indices of prime(n)^3 in A247834, or a(n)=0 if prime(n)^3 is not in A247834.

1, 0, 3, 4, 7, 9, 13, 15, 21, 27, 29, 37, 43, 47, 52, 61, 71, 74, 83, 89, 94, 105, 111, 123, 138, 145, 149, 158, 161, 168, 196, 208, 220, 226, 246, 248, 261, 276, 287, 299, 316, 319, 340, 345, 358, 364, 392, 422, 432, 436, 447, 464, 470, 496, 512, 530, 544, 549

Offset: 1

Vladimir Shevelev, Sep 24 2014

nonn

Conjecture: all a(n)>0, except for n=2.

			Using the formula, let us find the position in A247834, in which should be 17^3, if 17^3 belongs to A247834. Since 17 = prime(7), then we have a(7) = pi(17^(3/2)) - 6 = pi(70) - 6 = 13. Indeed, A247834(13) = 4913 = 17^3.

Cf. A030078, A156759, A247393, A247394, A247395, A247396, A247509, A247510, A247511, A247606, A247834, A247867.

a(n) = my(p=prime(n)); if(nextprime(ceil(p*sqrt(p))) > p*sqrt(prime(n+1)), 0, primepi(prime(n)^(3/2)) - n + 1); \\ Jinyuan Wang, Feb 17 2021

If prime(n)^3 is in A247834, then a(n) = pi(prime(n)^(3/2)) - n + 1, where pi(x) is the prime counting function (A000720).

More terms from Jinyuan Wang, Feb 17 2021

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

Original entry on oeis.org

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

Vladimir Shevelev, Sep 28 2014

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

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

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Vladimir Shevelev , A classification of the positive integers over primes

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

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

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

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).

cp's OEIS Frontend

A247835 Indices of prime(n)^3 in A247834, or a(n)=0 if prime(n)^3 is not in A247834.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

Extensions