A135369 a(0)=1, a(1)=2; thereafter, let n! = p(1)^b(1)...p(r)^b(r) be the prime factorization of n!. Then a(n) = Sum_{i=1..r} (p(i) + b(i)).

1, 2, 3, 7, 9, 15, 17, 25, 28, 30, 32, 44, 47, 61, 63, 65, 69, 87, 90, 110, 113, 115, 117, 141, 145, 147, 149, 152, 155, 185, 188, 220, 225, 227, 229, 231, 235, 273, 275, 277, 281, 323, 326, 370, 373, 376, 378, 426, 431, 433, 436, 438, 441, 495, 499, 501, 505

Offset: 0

Author

Ctibor O. Zizka, Feb 17 2008

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000142, A008474.

Programs

Maple

A001222 := proc(n) numtheory[bigomega](n) ; end:
A008472 := proc(n) add(op(1,i),i=ifactors(n)[2]) ; end:
A008474 := proc(n) A001222(n)+A008472(n) ; end:
A135369 := proc(n) if n < 2 then n+1 ; else A008474(n!) ; fi ; end: seq(A135369(n),n=0..80) ; # R. J. Mathar, Feb 28 2008

Mathematica

Join[{1},Table[Total[Flatten[FactorInteger[n!]]],{n,60}]] (* Harvey P. Dale, Feb 26 2012 *)

Formula

a(n) = A008474(n!) if n>1. - R. J. Mathar, Feb 28 2008

Extensions

More terms from R. J. Mathar, Feb 28 2008