

A111234


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


8



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
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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: A071324 A321441 A063655 * A117248 A079788 A146288
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



