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

%I A068319 #18 Feb 05 2018 03:01:17
%S A068319 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,
%T A068319 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,
%U A068319 31,59,11,61,3,3,19,11,5,67,5,5,37,71,7,73,7
%N A068319 a(n) = if n <= lpf(n)^2 then lpf(n) else a(lpf(n) + n/lpf(n)), where lpf = least prime factor, A020639.
%C A068319 n>1: a(n) is prime and a(n)=n iff n is prime.
%C A068319 a(n) = if n <= A088377(n) then A020639(n) else a(A111234(n)).
%H A068319 R. Zumkeller, <a href="/A068319/b068319.txt">Table of n, a(n) for n = 1..10000</a>
%e A068319 a(12)=a(2*6)=a(8)=a(2*4)=a(6)=a(2*3)=a(5)=a(5*1)=5.
%t A068319 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 *)
%o A068319 (Haskell)
%o A068319 a068319 n = if n <= spf ^ 2 then spf else a068319 $ spf + div n spf
%o A068319             where spf = a020639 n
%o A068319 -- _Reinhard Zumkeller_, Jun 24 2013
%Y A068319 Cf. A032742.
%K A068319 nonn,nice
%O A068319 1,2
%A A068319 _Reinhard Zumkeller_, Feb 27 2002, Jul 13 2007