

A038626


Smallest positive integer m such that m = pi(n*m) = A000720(n*m).


7



1, 9, 24, 66, 168, 437, 1051, 2614, 6454, 15927, 40071, 100346, 251706, 637197, 1617172, 4124436, 10553399, 27066969, 69709679, 179992838, 465769802, 1208198523, 3140421715, 8179002095, 21338685402, 55762149023, 145935689357, 382465573481, 1003652347080, 2636913002890, 6935812012540
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OFFSET

2,2


COMMENTS

Golomb shows that solutions exist for each n>1.
For all known terms, we have 2.4*a(n) < a(n+1) < 2.7*a(n) + 7. A038627(n) gives number of natural solutions of the equation m = pi(n*m).  Farideh Firoozbakht, Jan 09 2005
a(n) grows as exp(n)/n. Thus, a(n+1)/a(n) tends to e=exp(1) as n grows.  Max Alekseyev, Oct 15 2017


LINKS

Table of n, a(n) for n=2..32.
S. W. Golomb, On the Ratio of N to pi(N), American Mathematical Monthly, 69 (1962), 3637.
Eric Weisstein's World of Mathematics, Prime Counting Function.


FORMULA

a(n) = limit of f^(k)(1) as k grows, where f(x)=A000720(n*x). Also, a(n) = f^(A293529(n))(1).  Max Alekseyev, Oct 11 2017


EXAMPLE

pi(3059) = 437 and 3059/437 = 7, so a(7)=437.


CROSSREFS

Cf. A038623, A038624, A038625, A038627, A102281, A087237, A293529.
Sequence in context: A079770 A079771 A258438 * A195970 A223372 A180334
Adjacent sequences: A038623 A038624 A038625 * A038627 A038628 A038629


KEYWORD

nonn,changed


AUTHOR

Jud McCranie


EXTENSIONS

a(24) from Farideh Firoozbakht, Jan 09 2005
Edited by N. J. A. Sloane at the suggestion of Chris K. Caldwell, Apr 08 2008
a(25)a(32) from Max Alekseyev, Jul 18 2011, Oct 14 2017


STATUS

approved



