A256394 -id:A256394 - cp's OEIS frontend

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

N. J. A. Sloane, Nov 07 2000

nonn

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

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

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.

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

Apart from initial term same as A058011.

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

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

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

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

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

A057810 Quotients n/pi(n) for n in A057809.

Original entry on oeis.org

2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

N. J. A. Sloane, Nov 07 2000

Giovanni Resta, Table of n, a(n) for n = 1..1161

Cf. A000720, A057809, A038627, A256394.

(#/PrimePi[#] &) /@ Select[Range[2, 3*10^6], IntegerQ[#/PrimePi[#]] &] (* Michael De Vlieger, Apr 15 2015, after N. J. A. Sloane at A057809 *)

More terms from Naohiro Nomoto, Jun 26 2001

A071394 Numbers n divisible by pi(n) [A057809] with prime pi(n); i.e., largest prime factor of n equals pi(n).

Original entry on oeis.org

4, 6, 33, 335, 355, 3073, 8408, 64690, 481044, 1304693, 1304719, 3524318, 3524654, 9559785, 9559905, 70115803, 189963234, 189963918, 514278263, 1394194660, 3779856591, 10246935974, 75370122456, 204475052725, 204475053325, 1505578023783, 1505578024917

Offset: 1

Jason Earls, Jun 12 2002

nonn

			pi(8408) = 1051 and 8408 = 2*2*2*1051.

Giovanni Resta, Table of n, a(n) for n = 1..49

Cf. A000720, A006530, A256394.

c = 0; lpf[n_] := If[ PrimeQ[n], c++; n, Transpose[ FactorInteger[n]][[1, -1]]]; Do[ If[ lpf[n] == c, Print[n]], {n, 2, 10^7}]
Select[Select[Range[2,10^6],IntegerQ[#/PrimePi[#]]&],PrimeQ[PrimePi[#]]&] (* Ivan N. Ianakiev, Apr 15 2015 *)
Select[Range[10^6], FactorInteger[#][[-1, 1]] == PrimePi@ # &] (* Michael De Vlieger, Jul 30 2017 *)

isok(n) = isprime(p=primepi(n)) && !(n % p); \\ Michel Marcus, Jul 31 2017

A000720(a(n)) = A006530(a(n)) = A256394(n). - Jonathan Sondow, Apr 15 2015

Edited and extended by Robert G. Wilson v, Jun 13 2002
More terms from Hans Havermann, Jul 02 2002
a(26)-a(27) from Giovanni Resta, Mar 28 2017

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

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A057810 Quotients n/pi(n) for n in A057809.

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A071394 Numbers n divisible by pi(n) [A057809] with prime pi(n); i.e., largest prime factor of n equals pi(n).

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