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

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

1,1

Comments

Each cluster of entries is approximately a power of e from the previous cluster.

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.

Example

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

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 *)

Prog

(PARI) is(n)=n%primepi(n)==0 \\ Charles R Greathouse IV, Sep 14 2015
(Magma) [n: n in [2..10^5] | n mod #PrimesUpTo(n) eq 0]; // Vincenzo Librandi, Jul 04 2016

Crossrefs

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

Apart from initial term same as A058011.

Sequence in context: A222712 A117912 A092047 * A135632 A068541 A329887

Adjacent sequences: A057806 A057807 A057808 * A057810 A057811 A057812

Keyword

nonn

Author

N. J. A. Sloane, Nov 07 2000

Extensions

More terms from James A. Sellers, Nov 08 2000

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

Status

approved