OFFSET
1,4
COMMENTS
Also, number of primitive factors of 2^n - 1 (cf. A212953). - Max Alekseyev, May 03 2022
The multiplicative order of a mod m, gcd(a,m)=1, is the smallest natural number d for which a^d = 1 (mod m). See A002326.
a(n) is odd iff n is squarefree, A005117. - Thomas Ordowski, Jan 18 2014
The set S for which a(n) = |S| contains an odd number of prime powers p^k, where k > 0 and p == 3 (mod 4), iff n is squarefree and greater than one. - Isaac Saffold, Dec 28 2019
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..1206 (first 200 terms from Alois P. Heinz)
FORMULA
a(n) = Sum_{d|n} A008683(n/d) * A046801(d) = Sum_{d|A007947(n)} A008683(d) * A046801(n/d). - Max Alekseyev, May 03 2022
a(n) = 1 iff 2^n-1 is noncomposite. a(prime(n)) = 2^A088863(n)-1. - Thomas Ordowski, Jan 16 2014
EXAMPLE
a(3) = |{7}| = 1, a(4) = |{5,15}| = 2, a(6) = |{9,21,63}| = 3.
MAPLE
with(numtheory):
a:= n-> add(mobius(n/d)*tau(2^d-1), d=divisors(n)):
seq(a(n), n=1..100); # Alois P. Heinz, May 31 2012
MATHEMATICA
a[n_] := Sum[ MoebiusMu[n/d] * DivisorSigma[0, 2^d - 1], {d, Divisors[n]}]; Table[a[n], {n, 1, 71} ] (* Jean-François Alcover, Dec 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 04 2001
EXTENSIONS
More terms from John W. Layman, Mar 22 2002
More terms from Alois P. Heinz, May 31 2012
STATUS
approved