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A090387
Numerator of d(n)/n, where d(n) (A000005) is the number of divisors of n.
6
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
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
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