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!)
A301331 Number of compositions (ordered partitions) of n into parts having the same number of divisors as n. 2
1, 1, 1, 1, 1, 3, 1, 6, 1, 1, 1, 20, 1, 46, 3, 1, 1, 232, 1, 501, 1, 3, 9, 2352, 1, 6, 14, 6, 1, 24442, 1, 53243, 3, 16, 55, 32, 1, 550863, 107, 55, 1, 2616338, 1, 5701553, 6, 1, 406, 27077005, 1, 25, 9, 606, 9, 280237217, 3, 1244, 1, 1839, 3185, 2900328380, 1, 6320545915, 6248, 3, 1, 7828 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..65.

Index entries for sequences related to compositions

FORMULA

a(n) = [x^n] 1/(1 - Sum_{d(k) = d(n)} x^k).

EXAMPLE

a(14) = 3 because we have [14], [8, 6] and [6, 8], where 14, 8 and 6 are numbers with 4 divisors.

MAPLE

with(numtheory):

a:= proc(m) option remember; local k, b; k, b:= tau(m),

      proc(n) option remember; `if`(n=0, 1,

        add(`if`(tau(j)=k, b(n-j), 0), j=1..n))

      end: b(m)

    end:

seq(a(n), n=0..80);  # Alois P. Heinz, Mar 18 2018

MATHEMATICA

Table[SeriesCoefficient[1/(1 - Sum[Boole[DivisorSigma[0, k] == DivisorSigma[0, n]] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 65}]

CROSSREFS

Cf. A000005, A300977, A300978, A301332, A301333.

Sequence in context: A337604 A117782 A317855 * A301333 A213670 A116609

Adjacent sequences:  A301328 A301329 A301330 * A301332 A301333 A301334

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 18 2018

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 April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)