A064182 - OEIS

%I #51 Aug 18 2024 15:54:35

%S 0,11,171,2126,24300,266400,2853708,30130317,315037281,3271067968,

%T 33787242719,347589015681,3564432632541,36457601891708,

%U 372096179850464,3790896863469849,38562555830676602,391760068087338367,3975397006170581823,40066272402579605194

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

%C This is just a subsequence of A013939. - _N. J. A. Sloane_, Jul 16 2011

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

%F On the contrary, I guess that a(n) ~ 10^n * log n. - _Charles R Greathouse IV_, Jul 13 2011

%F a(n) ~ 10^n * (0.26149721284764278375 + log(log(10^n))). - _Hiroaki Yamanouchi_, Jul 10 2014

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

%o (PARI) a(n)=sum(k=1,10^n,omega(k)) \\ _Charles R Greathouse IV_, Jul 13 2011

%o (PARI) a(n)=sum(k=1,10^n\2,primepi(10^n\k)) \\ _Charles R Greathouse IV_, Jul 13 2011

%Y Cf. A001221, A013939.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Sep 20 2001

%E a(11)-a(13) from _Giovanni Resta_, Oct 26 2012

%E a(14)-a(16) from _Hiroaki Yamanouchi_, Jun 29 2014

%E a(17) from _Hiroaki Yamanouchi_, Jul 10 2014

%E a(18) from _Henri Lifchitz_, Aug 25 2014

%E a(19) from _Henri Lifchitz_, Dec 17 2017