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

1,2

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Sequence in context: A202840 A018153 A101687 * A341277 A049701 A005598

Adjacent sequences: A096458 A096459 A096460 * A096462 A096463 A096464

Keyword

nonn,nice

Author

Gil Broussard, Aug 12 2004

Extensions

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

Status

approved