A096461 a(1)=1, a(2)=2; for n >= 2, a(n+1) = a(n) + sum of prime factors of a(n).

1, 2, 4, 8, 14, 23, 46, 71, 142, 215, 263, 526, 791, 911, 1822, 2735, 3287, 3479, 3564, 3591, 3626, 3679, 3975, 4041, 4496, 4785, 4833, 5021, 10042, 15065, 15224, 15414, 15793, 16739, 17639, 18239, 18336, 18540, 18658, 19170, 19257, 19405, 23291

Offset: 1

Author

Gil Broussard, Aug 12 2004

Keywords

• nonn
• nice

Examples

			Given a(4)=8 whose prime factorization is 2*2*2, add to a(4) its prime factors (2+2+2)=6 to give a(5)=8+6=14.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Programs

Haskell

a096461 n = a096461_list !! (n-1)
a096461_list = 1 : iterate a075254 2  -- Reinhard Zumkeller, Feb 27 2012

Mathematica

a[1] := 1; a[n_] := a[n] = a[n - 1] + Plus@@Times@@@FactorInteger@a[n - 1]; Table[a[n], {n, 40}] (* Alonso del Arte, Jul 12 2011 *)
NestList[#+Total[Times@@@FactorInteger[#]]&,1,45] (* Harvey P. Dale, Nov 16 2011 *)

Formula

a(n+1) = A075254(a(n)) for n > 1. [Reinhard Zumkeller, Feb 27 2012]

Extensions

Definition corrected by N. J. A. Sloane, Jul 16 2007