A145834 a(n) = difference between the n-th composite number and the sum of its prime factors with repetition.

0, 1, 2, 3, 3, 5, 5, 7, 8, 10, 11, 11, 9, 15, 15, 11, 18, 17, 20, 22, 19, 15, 23, 26, 17, 23, 29, 30, 29, 34, 21, 37, 35, 38, 31, 35, 43, 39, 43, 35, 27, 48, 29, 50, 52, 47, 50, 47, 43, 56, 60, 35, 62, 53, 59, 60, 67, 69, 39, 70, 63, 41, 55, 71, 77, 71, 65, 59, 45, 71, 83, 82, 82

Offset: 1

Author

Alexander R. Povolotsky, Oct 20 2008

Keywords

• nonn

Examples

			a(1) = 4 - (2+2) = 0; a(2) = 6 - (2+3) = 1; a(3) = 8 - (2+2+2) = 2 ; a(4) = 9 - (3+3) = 3; a(5) = 10 - (2+5) = 3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A001414, A002808, A075255.

Programs

Mathematica

cnpf[n_]:=n-Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]; cnpf/@ Select[Range[100],CompositeQ] (* Harvey P. Dale, Aug 31 2021 *)

PARI

A145834(n)={for(k=0,primepi(n),isprime(n++)&k--);n+0-sum(i=1,#n=factor(n)~,n[1,i]*n[2,i])} \\ M. F. Hasler, Oct 31 2008

Formula

a(n) = A075255(A002808(n)) = A002808(n) - A001414(A002808(n)).

Extensions

Edited and extended by Ray Chandler, Oct 24 2008