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

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, 16, 30, 17, 32, 18, 14, 19, 12, 20, 38, 21, 16, 22, 42, 23, 44, 24, 18, 25, 48, 26, 14, 27, 20, 28, 54, 29, 16, 30, 22, 31, 60, 32, 62, 33, 24, 34, 18, 35, 68, 36, 26, 37, 72, 38, 74, 39

Offset: 1

Author

Leroy Quet, Oct 28 2005

Keywords

• nonn

Comments

If (but not only if) n is squarefree, then a(n) is coprime to n.

Largest semiperimeter of rectangle of area n. If n is prime, a(n) = n+1. - N. J. A. Sloane, Jun 14 2019

Examples

			12's largest proper divisor is 6. 12's smallest prime divisor is 2. So a(12) = 6 + 2 = 8.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032742, A020639, A068319, A063655.

Programs

Mathematica

f[n_] := Divisors[n][[ -2]] + FactorInteger[n][[1, 1]]; Table[ f[n], {n, 2, 74}] (* Robert G. Wilson v *)

PARI

a(n) = if (n==1, 2, my(p=factor(n)[1,1]); n/p + p); \\ Michel Marcus, Jun 14 2019

Python

from sympy import factorint
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

Formula

For all n >= 1, a(n) = A020639(n)+n/A020639(n). - N. J. A. Sloane, Jun 14 2019

Extensions

More terms from Robert G. Wilson v, Oct 31 2005

Added a(1) = 2. - N. J. A. Sloane, Jun 14 2019