

A059396


Number of primes less than square root of nth prime; i.e., number of trial divisions by smaller primes to show that nth prime is indeed prime.


2



0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9
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OFFSET

1,5


COMMENTS

Perhaps close to 2*(n/log(n))^(1/2).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A000720(A000196(A000040(n))).


EXAMPLE

a(32) = 5 since the 32nd prime is 131 which is not divisible by 2, 3, 5, 7 or 11 (and does not need to be tested against 13, 17, 19 etc. since 13^2 = 169 > 131).


MAPLE

a:= proc(n) option remember;
numtheory[pi](floor(sqrt(ithprime(n))))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Sep 05 2011


MATHEMATICA

Table[PrimePi[Sqrt[Prime[n]]], {n, 110}] (* Harvey P. Dale, Sep 06 2015 *)


CROSSREFS

Sequence in context: A178786 A000196 A111850 * A108602 A305025 A085290
Adjacent sequences: A059393 A059394 A059395 * A059397 A059398 A059399


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Jan 29 2001


STATUS

approved



