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A064182
Sum_{k <= 10^n} number of distinct primes dividing k (A001221).
3
0, 11, 171, 2126, 24300, 266400, 2853708, 30130317, 315037281, 3271067968, 33787242719, 347589015681, 3564432632541, 36457601891708, 372096179850464, 3790896863469849, 38562555830676602, 391760068087338367, 3975397006170581823, 40300330069855949801
OFFSET
0,2
COMMENTS
Subsequence of A013939. - N. J. A. Sloane, Jul 16 2011
LINKS
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
Sequence in context: A331929 A381219 A205087 * A139792 A025758 A243677
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
a(19) corrected by Henri Lifchitz, Oct 16 2025
STATUS
approved