|
|
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
(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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|