A123581 - OEIS

%I #15 Nov 07 2015 20:09:34

%S 3,6,9,12,15,20,25,30,35,42,49,56,63,70,77,88,99,110,121,132,143,156,

%T 169,182,195,208,221,238,255,272,289,306,323,342,361,380,399,418,437,

%U 460,483,506,529,552,575,598,621,644,667,696,725,754,783,812,841,870

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

%H Robert Israel, <a href="/A123581/b123581.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n+1) = A070229(a(n)). - _Reinhard Zumkeller_, Nov 07 2015

%e a(16) = 88 because a(15) is 77 whose largest prime factor is 11 so 77 + 11 = 88.

%p A123581:= proc(n) option remember;

%p local t;

%p t:= procname(n-1);

%p t + max(numtheory[factorset](t));

%p end proc;

%p A123581(1):= 3;

%p seq(A123581(n),n=1..100); # _Robert Israel_, May 18 2014

%t a[1] = 3; a[n_] := a[n] = a[n - 1] + FactorInteger[a[n - 1]][[ -1, 1]]; Array[a, 56] (* _Robert G. Wilson v_ *)

%o (PARI) {print1(a=3,",");for(n=2,57,print1(a=a+vecmax(factor(a)[,1]),","))} \\ _Klaus Brockhaus_, Nov 19 2006

%o (Haskell)

%o a123581 n = a123581_list !! (n-1)

%o a123581_list = iterate a070229 3  -- _Reinhard Zumkeller_, Nov 07 2015

%Y Essentially the same as A036441 and A076271.

%Y Cf. A070229.

%K nonn,easy

%O 1,1

%A _Ben Paul Thurston_, Nov 12 2006

%E More terms from _Robert G. Wilson v_ and _Klaus Brockhaus_, Nov 18 2006