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A111234 a(1)=2; thereafter a(n) = (largest proper divisor of n) + (smallest prime divisor of n).

%I A111234 #20 Jun 14 2019 14:22:00
%S A111234 2,3,4,4,6,5,8,6,6,7,12,8,14,9,8,10,18,11,20,12,10,13,24,14,10,15,12,
%T A111234 16,30,17,32,18,14,19,12,20,38,21,16,22,42,23,44,24,18,25,48,26,14,27,
%U A111234 20,28,54,29,16,30,22,31,60,32,62,33,24,34,18,35,68,36,26,37,72,38,74,39
%N A111234 a(1)=2; thereafter a(n) = (largest proper divisor of n) + (smallest prime divisor of n).
%C A111234 If (but not only if) n is squarefree, then a(n) is coprime to n.
%C A111234 Largest semiperimeter of rectangle of area n. If n is prime, a(n) = n+1. - _N. J. A. Sloane_, Jun 14 2019
%H A111234 Chai Wah Wu, <a href="/A111234/b111234.txt">Table of n, a(n) for n = 1..10000</a>
%F A111234 For all n >= 1, a(n) = A020639(n)+n/A020639(n). - _N. J. A. Sloane_, Jun 14 2019
%e A111234 12's largest proper divisor is 6. 12's smallest prime divisor is 2. So a(12) = 6 + 2 = 8.
%t A111234 f[n_] := Divisors[n][[ -2]] + FactorInteger[n][[1, 1]]; Table[ f[n], {n, 2, 74}] (* _Robert G. Wilson v_ *)
%o A111234 (Python)
%o A111234 from sympy import factorint
%o A111234 A111234_list = [2] + [a+b//a for a, b in ((min(factorint(n)), n) for n in range(2,10001))] # _Chai Wah Wu_, Jun 14 2019
%o A111234 (PARI) a(n) = if (n==1, 2, my(p=factor(n)[1,1]); n/p + p); \\ _Michel Marcus_, Jun 14 2019
%Y A111234 Cf. A032742, A020639, A068319, A063655.
%K A111234 nonn
%O A111234 1,1
%A A111234 _Leroy Quet_, Oct 28 2005
%E A111234 More terms from _Robert G. Wilson v_, Oct 31 2005
%E A111234 Added a(1) = 2. - _N. J. A. Sloane_, Jun 14 2019