A334762 a(n) = ceiling (n / A000005(n)).

1, 1, 2, 2, 3, 2, 4, 2, 3, 3, 6, 2, 7, 4, 4, 4, 9, 3, 10, 4, 6, 6, 12, 3, 9, 7, 7, 5, 15, 4, 16, 6, 9, 9, 9, 4, 19, 10, 10, 5, 21, 6, 22, 8, 8, 12, 24, 5, 17, 9, 13, 9, 27, 7, 14, 7, 15, 15

Offset: 1

Author

Ctibor O. Zizka, May 10 2020

Keywords

• nonn
• look

Comments

ceiling (n / A000005(n)) - floor (n / A000005(n)) = 0 for A033950(n).

Examples

			a(1) = ceiling (1 / 1) = 1;
a(5) = ceiling (5 / 2) = 3;
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A033950, A078709.

Programs

Maple

seq(ceil(n/numtheory:-tau(n)), n=1..100); # Robert Israel, May 13 2020

Mathematica

a[n_] := Ceiling[n / DivisorSigma[0, n]]; Array[a, 60] (* Amiram Eldar, May 10 2020 *)

Python

from sympy import divisor_count
def A334762(n): return (a := divmod(n,divisor_count(n)))[0] + int((a[1] > 0) == True) # Chai Wah Wu, Jun 20 2022

Formula

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