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a(1)=1, a(2)=2; for n >= 2, a(n+1) = a(n) + sum of prime factors of a(n).
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%I #25 Oct 04 2014 03:24:26

%S 1,2,4,8,14,23,46,71,142,215,263,526,791,911,1822,2735,3287,3479,3564,

%T 3591,3626,3679,3975,4041,4496,4785,4833,5021,10042,15065,15224,15414,

%U 15793,16739,17639,18239,18336,18540,18658,19170,19257,19405,23291

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

%H T. D. Noe, <a href="/A096461/b096461.txt">Table of n, a(n) for n=1..1000</a>

%F a(n+1) = A075254(a(n)) for n > 1. [_Reinhard Zumkeller_, Feb 27 2012]

%e 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.

%t 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 *)

%t NestList[#+Total[Times@@@FactorInteger[#]]&,1,45] (* _Harvey P. Dale_, Nov 16 2011 *)

%o (Haskell)

%o a096461 n = a096461_list !! (n-1)

%o a096461_list = 1 : iterate a075254 2 -- _Reinhard Zumkeller_, Feb 27 2012

%K nonn,nice

%O 1,2

%A _Gil Broussard_, Aug 12 2004

%E Definition corrected by _N. J. A. Sloane_, Jul 16 2007