cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A194895 Difference between the number of semiprimes less than 10^n and the number of primes less than 10^n.

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%I A194895 #14 Jul 22 2025 12:38:16
%S A194895 0,-1,9,131,1396,13786,131537,1239745,11665803,109941002,1038723932,
%T A194895 9841935529,93518105160,891022511814,8510960557278,81485246876212,
%U A194895 781818951793344
%N A194895 Difference between the number of semiprimes less than 10^n and the number of primes less than 10^n.
%C A194895 A066265 minus A006880
%e A194895 There are 2625 semiprimes less than 10^4 and there are 1229 primes less than 10^4, so a(4) = 2625 - 1229 = 1396.
%t A194895 SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] - i + 1, {i, PrimePi@ Sqrt@ n}]; f[n_] := SemiPrimePi[10^n - 1] - PrimePi[10^n - 1]; Array[f, 15, 0] (* _Robert G. Wilson v_, Jul 05 2012 *)
%Y A194895 Cf. A006880, A066265
%K A194895 sign
%O A194895 0,3
%A A194895 _Harvey P. Dale_, Sep 04 2011