A057809 Numbers k such that pi(k) divides k.

2, 4, 6, 8, 27, 30, 33, 96, 100, 120, 330, 335, 340, 350, 355, 360, 1008, 1080, 1092, 1116, 1122, 1128, 1134, 3059, 3066, 3073, 3080, 3087, 3094, 8408, 8424, 8440, 8456, 8464, 8472, 23526, 23535, 24300, 64540, 64580, 64610, 64620, 64650, 64690, 64700

Offset: 1

Author

N. J. A. Sloane, Nov 07 2000

Keywords

• nonn

Comments

Each cluster of entries is approximately a power of e times larger than the previous cluster.

The sequence is infinite (Golomb, 1962). - Yifan Xie, Jun 23 2025

Examples

			120 is a member as there are exactly 30 primes less than 120 and 30 * 4 = 120.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1161 (first 296 terms from Charles R Greathouse IV)
• Konstantinos N. Gaitanas, An explicit formula for the prime counting function, arXiv preprint arXiv:1311.1398 [math.NT], 2013.
• S. W. Golomb, On the Ratio of N to π(N), The American Mathematical Monthly 69.1 (1962): 36-37.

Crossrefs

Cf. A000720, A057810, A071394, A038627, A256394.

Apart from initial term same as A058011.

Programs

Magma

[n: n in [2..10^5] | n mod #PrimesUpTo(n) eq 0]; // Vincenzo Librandi, Jul 04 2016

Maple

select(t -> t mod numtheory:-pi(t) = 0, [$2..10^5]); # Robert Israel, Jul 03 2016

Mathematica

Select[ Range[2, 10^5], IntegerQ[ # / PrimePi[ # ]] & ]
Select[Range[1000], Divisible[#, PrimePi[#]] &] (* Requires version 6.0+. Alonso del Arte, May 24 2015 *)

PARI

is(n)=n%primepi(n)==0 \\ Charles R Greathouse IV, Sep 14 2015

Extensions

More terms from James Sellers, Nov 08 2000

a(297)-a(1161) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Aug 31 2018