

A207329


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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: A308828 A325683 A057767 * A122977 A275870 A321721
Adjacent sequences: A207326 A207327 A207328 * A207330 A207331 A207332


KEYWORD

nonn


AUTHOR

Ben Branman, Feb 27 2012


STATUS

approved



