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A123581 a(1) = 3, a(n) = a(n-1) + greatest prime factor of a(n-1).

%I A123581 #15 Nov 07 2015 20:09:34
%S A123581 3,6,9,12,15,20,25,30,35,42,49,56,63,70,77,88,99,110,121,132,143,156,
%T A123581 169,182,195,208,221,238,255,272,289,306,323,342,361,380,399,418,437,
%U A123581 460,483,506,529,552,575,598,621,644,667,696,725,754,783,812,841,870
%N A123581 a(1) = 3, a(n) = a(n-1) + greatest prime factor of a(n-1).
%H A123581 Robert Israel, <a href="/A123581/b123581.txt">Table of n, a(n) for n = 1..10000</a>
%F A123581 a(n+1) = A070229(a(n)). - _Reinhard Zumkeller_, Nov 07 2015
%e A123581 a(16) = 88 because a(15) is 77 whose largest prime factor is 11 so 77 + 11 = 88.
%p A123581 A123581:= proc(n) option remember;
%p A123581 local t;
%p A123581 t:= procname(n-1);
%p A123581 t + max(numtheory[factorset](t));
%p A123581 end proc;
%p A123581 A123581(1):= 3;
%p A123581 seq(A123581(n),n=1..100); # _Robert Israel_, May 18 2014
%t A123581 a[1] = 3; a[n_] := a[n] = a[n - 1] + FactorInteger[a[n - 1]][[ -1, 1]]; Array[a, 56] (* _Robert G. Wilson v_ *)
%o A123581 (PARI) {print1(a=3,",");for(n=2,57,print1(a=a+vecmax(factor(a)[,1]),","))} \\ _Klaus Brockhaus_, Nov 19 2006
%o A123581 (Haskell)
%o A123581 a123581 n = a123581_list !! (n-1)
%o A123581 a123581_list = iterate a070229 3  -- _Reinhard Zumkeller_, Nov 07 2015
%Y A123581 Essentially the same as A036441 and A076271.
%Y A123581 Cf. A070229.
%K A123581 nonn,easy
%O A123581 1,1
%A A123581 _Ben Paul Thurston_, Nov 12 2006
%E A123581 More terms from _Robert G. Wilson v_ and _Klaus Brockhaus_, Nov 18 2006