A090387 Numerator of d(n)/n, where d(n) (A000005) is the number of divisors of n.

1, 1, 2, 3, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 4, 5, 2, 1, 2, 3, 4, 2, 2, 1, 3, 2, 4, 3, 2, 4, 2, 3, 4, 2, 4, 1, 2, 2, 4, 1, 2, 4, 2, 3, 2, 2, 2, 5, 3, 3, 4, 3, 2, 4, 4, 1, 4, 2, 2, 1, 2, 2, 2, 7, 4, 4, 2, 3, 4, 4, 2, 1, 2, 2, 2, 3, 4, 4, 2, 1, 5, 2, 2, 1, 4, 2, 4, 1, 2, 2, 4, 3, 4, 2, 4, 1, 2, 3, 2, 9, 2, 4, 2, 1, 8

Offset

1,3

Comments

Values of n at which k first occurs, for k >= 1: 1, 3, 4, 15, 16, 175, 64, 105, 100, 567, 1024, 1925, 4096, 3645, 784, 945, 65536, ... - Robert G. Wilson v, Feb 04 2004. [Is this A136641? - Editors]

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

a(6)=2 because the number of divisors of 6 is 4 and 4 divided by 6 equals 2/3, which has 2 as its numerator.

Maple

with(numtheory): seq(numer(tau(n)/n), n=1..105) ; # Zerinvary Lajos, Jun 04 2008

Prog

(PARI) A090387(n) = numerator(numdiv(n)/n); \\ Antti Karttunen, Sep 25 2018
(Python)
from math import gcd
from sympy import divisor_count
def A090387(n): return (d := divisor_count(n))//gcd(n, d) # Chai Wah Wu, Jun 20 2022

Crossrefs

Cf. A000005, A090395 (denominators), A136641.

Sequence in context: A334052 A160570 A128830 * A030329 A300139 A300666

Adjacent sequences: A090384 A090385 A090386 * A090388 A090389 A090390

Keyword

easy,frac,nonn

Author

Ivan_E_Mayle(AT)a_provider.com, Jan 31 2004

Extensions

More terms from Robert G. Wilson v, Feb 04 2004

Status

approved