OFFSET
1,1
COMMENTS
a(n) is the largest prime factor of n, since pi(n) ~ n / log n.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..49
K. Gaitanas, An explicit formula for the prime counting function, arXiv:1311.1398 [math.NT], 2013.
K. Gaitanas, An Explicit Formula for the Prime Counting Function Which is Valid Infinitely Often, Amer. Math. Monthly, 122 (2015), 283.
S. W. Golomb, On the Ratio of N to pi(N), American Mathematical Monthly, 69 (1962), 36-37.
R. T. Harger and W. L. Hightower, An Interesting Property of x/pi(x), College Math. J., 40 (2009), 213-214.
Eric Weisstein's World of Mathematics, Prime Counting Function
EXAMPLE
pi(6) = 3 is prime, and 3 divides 6, so 3 is a member.
MATHEMATICA
c = 0; lpf[n_] := If[ PrimeQ[n], c++; n, Transpose[ FactorInteger[n]][[1, -1]]]; Do[ If[lpf[n] == c, Print[ PrimePi[n]]], {n, 2, 10^7}]
PrimePi[Select[Select[Range[2, 10^6], IntegerQ[#/PrimePi[#]]&], PrimeQ[PrimePi[#]]&]] (* Ivan N. Ianakiev, Apr 15 2015 *)
Select[Table[{PrimePi[n], n}, {n, 10^6}], PrimeQ[#[[1]]]&&Divisible[#[[2]], #[[1]]]&][[All, 1]] (* The program generates the first 9 terms of the sequence. To generate more, increase the constant for n. *) (* Harvey P. Dale, Feb 08 2022 *)
PROG
(PARI) for(n=1, 10^6, if(isprime(p=primepi(n))&&!(n%primepi(n)), print1(p, ", "))) \\ Derek Orr, Apr 14 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Apr 13 2015
EXTENSIONS
More terms from Giovanni Resta, Sep 01 2018
STATUS
approved