OFFSET
1,3
COMMENTS
The first occurrence of k (if it exists) is studied in A091895.
Sequence A353011 gives indices of "late birds": n such that a(k) > a(n) for all k > n. - M. F. Hasler, Apr 15 2022
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537
FORMULA
a(n) = n/g with g = A009191(n) = gcd(A000005(n), n). This explains the "rays" in the graph, e.g., g = 1 for odd squarefree n, g = 2 for even semiprimes n = 2p > 4 and n = 4p, p > 3. - M. F. Hasler, Apr 15 2022
EXAMPLE
a(6) = 3 because the number of divisors of 6 is 4 and 4 divided by 6 equals 2/3, which has 3 as its denominator.
MAPLE
with(numtheory): seq(denom(tau(n)/n), n=1..75) ; # Zerinvary Lajos, Jun 04 2008
MATHEMATICA
Table[ Denominator[ DivisorSigma[0, n]/n], {n, 1, 80}] (* Robert G. Wilson v, Feb 04 2004 *)
PROG
(PARI) A090395(n) = denominator(numdiv(n)/n); \\ Antti Karttunen, Sep 25 2018
(Python)
from math import gcd
from sympy import divisor_count
def A090395(n): return n//gcd(n, divisor_count(n)) # Chai Wah Wu, Jun 20 2022
CROSSREFS
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