A064182 Sum_{k <= 10^n} number of distinct primes dividing k (A001221).

0, 11, 171, 2126, 24300, 266400, 2853708, 30130317, 315037281, 3271067968, 33787242719, 347589015681, 3564432632541, 36457601891708, 372096179850464, 3790896863469849, 38562555830676602, 391760068087338367, 3975397006170581823, 40066272402579605194

Offset

0,2

Comments

This is just a subsequence of A013939. - N. J. A. Sloane, Jul 16 2011

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k, 1, limit}, PrimePi(10^n/k); which seems to be about 10^n/2.

On the contrary, I guess that a(n) ~ 10^n * log n. - Charles R Greathouse IV, Jul 13 2011

a(n) ~ 10^n * (0.26149721284764278375 + log(log(10^n))). - Hiroaki Yamanouchi, Jul 10 2014

Mathematica

s = 0; k = 2; Do[ While[ k <= 10^n, s = s + PrimeNu@ k; k++ ]; Print[ s], {n, 8}]

Prog

(PARI) a(n)=sum(k=1, 10^n, omega(k)) \\ Charles R Greathouse IV, Jul 13 2011
(PARI) a(n)=sum(k=1, 10^n\2, primepi(10^n\k)) \\ Charles R Greathouse IV, Jul 13 2011

Crossrefs

Cf. A001221, A013939.

Sequence in context: A167245 A331929 A205087 * A139792 A025758 A243677

Adjacent sequences: A064179 A064180 A064181 * A064183 A064184 A064185

Keyword

nonn

Author

Robert G. Wilson v, Sep 20 2001

Extensions

a(11)-a(13) from Giovanni Resta, Oct 26 2012

a(14)-a(16) from Hiroaki Yamanouchi, Jun 29 2014

a(17) from Hiroaki Yamanouchi, Jul 10 2014

a(18) from Henri Lifchitz, Aug 25 2014

a(19) from Henri Lifchitz, Dec 17 2017

Status

approved