login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Total number of composite numbers with n digits and n prime factors (counted with multiplicity).
4

%I #16 Jun 19 2022 12:52:41

%S 0,31,225,1563,10222,63030,374264,2160300,12196405,67724342,371233523,

%T 2014305995

%N Total number of composite numbers with n digits and n prime factors (counted with multiplicity).

%C Essentially the same as A124033.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_025.htm">Puzzle 25. Composed primes (by G.L. Honaker, Jr.)</a>, The Prime Puzzles and Problems Connection. (A related puzzle.)

%e a(1) = 0, since any single-digit number with 1 prime factor is a prime!

%t Table[Total[Table[If[CompositeQ[n]&&PrimeOmega[n]==x,1,0],{n,10^(x-1),10^x-1}]],{x,8}] (* The program generates the first 8 terms of the sequence. *) (* _Harvey P. Dale_, Jun 19 2022 *)

%Y Cf. A036336, A036337, A036338.

%K nonn,base,more

%O 1,2

%A _Patrick De Geest_, Dec 15 1998

%E One more term from _Naohiro Nomoto_, Jul 31 2001

%E a(9)-a(12) from _Ray Chandler_, Apr 12 2011