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

3, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 70, 77, 88, 99, 110, 121, 132, 143, 156, 169, 182, 195, 208, 221, 238, 255, 272, 289, 306, 323, 342, 361, 380, 399, 418, 437, 460, 483, 506, 529, 552, 575, 598, 621, 644, 667, 696, 725, 754, 783, 812, 841, 870

Offset: 1

Author

Ben Paul Thurston, Nov 12 2006

Keywords

• nonn
• easy

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Essentially the same as A036441 and A076271.

Cf. A070229.

Programs

Haskell

a123581 n = a123581_list !! (n-1)
a123581_list = iterate a070229 3  -- Reinhard Zumkeller, Nov 07 2015

Maple

A123581:= proc(n) option remember;
local t;
t:= procname(n-1);
t + max(numtheory[factorset](t));
end proc;
A123581(1):= 3;
seq(A123581(n),n=1..100); # Robert Israel, May 18 2014

Mathematica

a[1] = 3; a[n_] := a[n] = a[n - 1] + FactorInteger[a[n - 1]][[ -1, 1]]; Array[a, 56] (* Robert G. Wilson v *)

PARI

{print1(a=3,",");for(n=2,57,print1(a=a+vecmax(factor(a)[,1]),","))} \\ Klaus Brockhaus, Nov 19 2006

Formula

a(n+1) = A070229(a(n)). - Reinhard Zumkeller, Nov 07 2015

Extensions

More terms from Robert G. Wilson v and Klaus Brockhaus, Nov 18 2006