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

%I A057809 #48 Jul 02 2025 16:02:00
%S A057809 2,4,6,8,27,30,33,96,100,120,330,335,340,350,355,360,1008,1080,1092,
%T A057809 1116,1122,1128,1134,3059,3066,3073,3080,3087,3094,8408,8424,8440,
%U A057809 8456,8464,8472,23526,23535,24300,64540,64580,64610,64620,64650,64690,64700
%N A057809 Numbers k such that pi(k) divides k.
%C A057809 Each cluster of entries is approximately a power of e times larger than the previous cluster.
%C A057809 The sequence is infinite (Golomb, 1962). - _Yifan Xie_, Jun 23 2025
%H A057809 Giovanni Resta, <a href="/A057809/b057809.txt">Table of n, a(n) for n = 1..1161</a> (first 296 terms from Charles R Greathouse IV)
%H A057809 Konstantinos N. Gaitanas, <a href="http://arxiv.org/abs/1311.1398">An explicit formula for the prime counting function</a>, arXiv preprint arXiv:1311.1398 [math.NT], 2013.
%H A057809 S. W. Golomb, <a href="http://www.jstor.org/stable/2312732">On the Ratio of N to π(N)</a>, The American Mathematical Monthly 69.1 (1962): 36-37.
%e A057809 120 is a member as there are exactly 30 primes less than 120 and 30 * 4 = 120.
%p A057809 select(t -> t mod numtheory:-pi(t) = 0, [$2..10^5]); # _Robert Israel_, Jul 03 2016
%t A057809 Select[ Range[2, 10^5], IntegerQ[ # / PrimePi[ # ]] & ]
%t A057809 Select[Range[1000], Divisible[#, PrimePi[#]] &] (* Requires version 6.0+. _Alonso del Arte_, May 24 2015 *)
%o A057809 (PARI) is(n)=n%primepi(n)==0 \\ _Charles R Greathouse IV_, Sep 14 2015
%o A057809 (Magma) [n: n in [2..10^5] | n mod #PrimesUpTo(n) eq 0]; // _Vincenzo Librandi_, Jul 04 2016
%Y A057809 Cf. A000720, A057810, A071394, A038627, A256394.
%Y A057809 Apart from initial term same as A058011.
%K A057809 nonn
%O A057809 1,1
%A A057809 _N. J. A. Sloane_, Nov 07 2000
%E A057809 More terms from _James Sellers_, Nov 08 2000
%E A057809 a(297)-a(1161) obtained from the values of A038625 computed by _Jan Büthe_. - _Giovanni Resta_, Aug 31 2018