A068319 a(n) = if n <= lpf(n)^2 then lpf(n) else a(lpf(n) + n/lpf(n)), where lpf = least prime factor, A020639.

1, 2, 3, 2, 5, 5, 7, 5, 3, 7, 11, 5, 13, 3, 5, 7, 17, 11, 19, 5, 7, 13, 23, 3, 5, 5, 5, 7, 29, 17, 31, 11, 3, 19, 5, 5, 37, 7, 7, 13, 41, 23, 43, 3, 11, 5, 47, 5, 7, 5, 5, 7, 53, 29, 7, 17, 13, 31, 59, 11, 61, 3, 3, 19, 11, 5, 67, 5, 5, 37, 71, 7, 73, 7

Offset: 1

Author

Reinhard Zumkeller, Feb 27 2002, Jul 13 2007

Keywords

• nonn
• nice

Comments

n>1: a(n) is prime and a(n)=n iff n is prime.

a(n) = if n <= A088377(n) then A020639(n) else a(A111234(n)).

Examples

			a(12)=a(2*6)=a(8)=a(2*4)=a(6)=a(2*3)=a(5)=a(5*1)=5.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032742.

Programs

Haskell

a068319 n = if n <= spf ^ 2 then spf else a068319 $ spf + div n spf
            where spf = a020639 n
-- Reinhard Zumkeller, Jun 24 2013

Mathematica

lpf[n_] := FactorInteger[n][[1, 1]]; a[n_] := a[n] = If[n <= lpf[n]^2, lpf[n], a[lpf[n] + n/lpf[n]]]; Table[a[n], {n, 1, 74}](* Jean-François Alcover, Dec 21 2011 *)