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

1,2

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)).

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A032742.

Sequence in context: A074251 A074196 A153023 * A133775 A099043 A318677

Adjacent sequences: A068316 A068317 A068318 * A068320 A068321 A068322

Keyword

nonn,nice

Author

Reinhard Zumkeller, Feb 27 2002, Jul 13 2007

Status

approved