A207329 Number of distinct integers which can be represented as the product of factors of n, using each factor at most once.

1, 2, 2, 4, 2, 7, 2, 7, 4, 7, 2, 20, 2, 7, 7, 11, 2, 20, 2, 20, 7, 7, 2, 45, 4, 7, 7, 20, 2, 59, 2, 16, 7, 7, 7, 66, 2, 7, 7, 45, 2, 59, 2, 20, 20, 7, 2, 86, 4, 20, 7, 20, 2, 45, 7, 45, 7, 7, 2, 269, 2, 7, 20, 22, 7, 59, 2, 20, 7, 59, 2, 157, 2, 7, 20, 20, 7

Offset

1,2

Comments

a(n) depends only on the prime signature of n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Formula

For prime p, a(p^n) = A000124(n) (independently of p).

a(n) = A069625(n) + 1. - Michel Marcus, Sep 17 2013

Example

For n=4, n has factors 1, 2, and 4, which can be multiplied to yield 1, 2, 4, or 8, thus a(4)=4.

Mathematica

a[n_] := Length[DeleteDuplicates[Times @@@ Subsets[Divisors[n]]]]; Table[a[n], {n, 100}]

Crossrefs

Cf. A000124, A007955.

Sequence in context: A325683 A331121 A057767 * A348219 A122977 A275870

Adjacent sequences: A207326 A207327 A207328 * A207330 A207331 A207332

Keyword

nonn

Author

Ben Branman, Feb 27 2012

Status

approved