A355140 n/d(n) rounded to the nearest integer, where d(n) is the number of divisors of n (A000005).

1, 1, 2, 1, 3, 2, 4, 2, 3, 3, 6, 2, 7, 4, 4, 3, 9, 3, 10, 3, 5, 6, 12, 3, 8, 7, 7, 5, 15, 4, 16, 5, 8, 9, 9, 4, 19, 10, 10, 5, 21, 5, 22, 7, 8, 12, 24, 5, 16, 8, 13, 9, 27, 7, 14, 7, 14, 15, 30, 5, 31, 16, 11, 9, 16, 8, 34, 11, 17, 9, 36, 6, 37, 19, 13, 13, 19

Offset: 1

Author

Sameer Khan, Jun 20 2022

Keywords

• nonn

Comments

In the ambiguous case, fractions are rounded up.

Examples

			a(1) = round (1 / 1) = 1;
a(4) = round (4 / 3) = 1;
a(5) = round (5 / 2) = 3;
		

Crossrefs

Cf. A000005, A078709 (floor), A334762 (ceiling), A090395 (numerators), A090387 (denominators).

Programs

Mathematica

Table[Floor[n/DivisorSigma[0,n]+1/2],{n,100}] (* Harvey P. Dale, Dec 22 2022 *)

Python

from sympy import divisor_count
def A355140(n): return (2*n+(d:=divisor_count(n)))//(2*d) # Chai Wah Wu, Jun 20 2022

Formula

a(n) = round (n / A000005(n)).