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Number of semiprimes among n-th million natural numbers.
1

%I #15 Mar 15 2015 18:59:12

%S 210035,197249,193162,190540,188288,187308,185657,184788,183856,

%T 183441,182123,181556,181125,180878,180234,179649,179055,178710,

%U 178652,178034,178015,177307,177391,177003,176568,176419,176021,175788,175655,175189,174915,175357

%N Number of semiprimes among n-th million natural numbers.

%C Let f(m) = number of semiprimes <m then a(n) is the number of semiprimes between 1+(n-1)*10^6 and n*10^6.

%C a(n) = 0 for almost all n. It seems infeasible to find the first such n. - _Charles R Greathouse IV_, Sep 09 2012

%H Zak Seidov, <a href="/A216593/b216593.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ 1000000 n log log n / log n. - _Charles R Greathouse IV_, Sep 23 2012

%t f[m_] := Sum[ PrimePi[(m - 1)/Prime[i]], {i, PrimePi[ Sqrt[m]]}] - Binomial[ PrimePi[ Sqrt[m]], 2]; ta=Table[f[n*10^6],{n,0,1000}];s=Rest[ta]-Most[ta] (* for first 1000 terms *)

%t (* using Mmca code by _Robert G. Wilson v_ in A066265 - _Zak Seidov_, Sep 09 2012 *)

%o (PARI) a(n)=sum(k=10^6*(n-1),10^6*n,bigomega(k)==2) \\ _Charles R Greathouse IV_, Sep 09 2012

%Y Cf. A001358, A036352, A064911, A066265, A072000.

%K nonn

%O 1,1

%A _Zak Seidov_, Sep 09 2012