|
| |
|
|
A073184
|
|
Number of cube-free divisors of n.
|
|
4
| |
|
|
1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 3, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 3, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 6, 3, 4, 2, 12, 4, 4, 4, 6, 2, 12, 4, 6, 4, 4, 4, 6, 2, 6, 6, 9, 2, 8, 2
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| a(n) = sum of divisors of the cube-free kernel of n: a(n)=A073184(A007948(n));
a(n) <= A073182(n).
Multiplicative because it is the Inverse Moebius transform of the characteristic function of cube-free numbers. a(n) is a prime signature sequence. a(p) = 2, a(p^e) = 3, e>1. Christian G. Bower (bowerc(AT)usa.net) May 18, 2005.
|
|
|
FORMULA
| Dirichlet g.f. zeta(s)^2/zeta(3*s). Dirichlet convolution of the characteristic function of cube-free numbers by A000012. - R. J. Mathar, Apr 12 2011
|
|
|
EXAMPLE
| The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, 8=2^3 and 56=7*2^3 are not cube-free, therefore a(56)=6.
|
|
|
CROSSREFS
| Cf. A000005, A073185, A004709, A073183, A073180, A034444.
Sequence in context: A205562 A196437 A106491 * A073182 A049599 A043261
Adjacent sequences: A073181 A073182 A073183 * A073185 A073186 A073187
|
|
|
KEYWORD
| nonn,mult
|
|
|
AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 19 2002
|
| |
|
|
