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 A059396 Number of primes less than square root of n-th prime; i.e., number of trial divisions by smaller primes to show that n-th 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Asymptotic to 2*(n/log(n))^(1/2): Since p_n ~ n * log n, a(n) ~ sqrt(n * log n) / (log (sqrt(n * log n))) ~ 2 * sqrt(n) * sqrt(log n) / (log n + log log n) ~ 2 * sqrt(n / log n). - Daniel Forgues, Sep 04 2018 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 *) PROG (PARI) a(n) = primepi(sqrtint(prime(n))); \\ Altug Alkan, Sep 05 2018 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

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Last modified November 20 08:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)