A111234 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

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

CROSSREFS

Cf. A032742, A020639, A068319, A063655.

Sequence in context: A361003 A321441 A063655 * A117248 A373624 A343292

Adjacent sequences: A111231 A111232 A111233 * A111235 A111236 A111237

KEYWORD

nonn

AUTHOR

Leroy Quet, Oct 28 2005

EXTENSIONS

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

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

STATUS

approved