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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

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)