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A256394 Prime values of pi(n) that divide n. 4
2, 3, 11, 67, 71, 439, 1051, 6469, 40087, 100361, 100363, 251737, 251761, 637319, 637327, 4124459, 10553513, 10553551, 27067277, 69709733, 179993171, 465769817, 3140421769, 8179002109, 8179002133, 55762149029, 55762149071, 382465573489, 1003652347081 (list; graph; refs; listen; history; text; internal format)
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

FORMULA

a(n) = A000720(A071394(n)) = A006530(A071394(n)).

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 *)

PROG

(PARI) for(n=1, 10^6, if(isprime(p=primepi(n))&&!(n%primepi(n)), print1(p, ", "))) \\ Derek Orr, Apr 14 2015

CROSSREFS

Cf. A000720, A006530, A038623-A038627, A057809, A057810, A071394, A087235-A087241.

Sequence in context: A105217 A066046 A065597 * A219513 A001052 A184310

Adjacent sequences:  A256391 A256392 A256393 * A256395 A256396 A256397

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Apr 13 2015

EXTENSIONS

More terms from Giovanni Resta, Sep 01 2018

STATUS

approved

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Last modified October 30 18:13 EDT 2020. Contains 338090 sequences. (Running on oeis4.)