login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327658 Number of factorizations of n that are empty or whose factors have a common divisor > 1. 2
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 1, 2, 1, 2, 1, 1, 1, 4, 2, 1, 3, 2, 1, 1, 1, 7, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 2, 2, 1, 1, 7, 2, 2, 1, 2, 1, 4, 1, 4, 1, 1, 1, 3, 1, 1, 2, 11, 1, 1, 1, 2, 1, 1, 1, 7, 1, 1, 2, 2, 1, 1, 1, 7, 5, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

First differs from A319786 at a(900) = 11, A319786(900) = 12.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices have a common divisor > 1 are listed in A318978.

LINKS

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

The a(120) = 7 factorizations:

  (120)

  (2*60)

  (4*30)

  (6*20)

  (10*12)

  (2*2*30)

  (2*6*10)

MATHEMATICA

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

Table[Length[Select[facs[n], #=={}||GCD@@#!=1&]], {n, 100}]

CROSSREFS

See link for additional cross-references.

Cf. A000005, A056239, A112798, A281116, A289509, A327406.

Sequence in context: A322453 A327012 A328855 * A319786 A321271 A305193

Adjacent sequences:  A327655 A327656 A327657 * A327659 A327660 A327661

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 21 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 29 18:30 EDT 2020. Contains 338067 sequences. (Running on oeis4.)