login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A218002 E.g.f.: exp( Sum_{n>=1} x^prime(n) / prime(n) ). 6
1, 0, 1, 2, 3, 44, 55, 1434, 3913, 39752, 392481, 5109290, 34683451, 914698212, 5777487703, 91494090674, 1504751645265, 31764834185744, 379862450767873, 12634073744624082, 132945783064464691, 2753044719709341980, 64135578414076991031, 1822831113987975441482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Conjecture: a(n) = number of degree-n permutations of prime order.

The conjecture is false. Cf. A214003. This sequence gives the number of n-permutations whose cycle lengths are restricted to the prime numbers. - Geoffrey Critzer, Nov 08 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

EXAMPLE

E.g.f.: A(x) = 1 + x^2/2! + 2*x^3/3! + 3*x^4/4! + 44*x^5/5! + 55*x^6/6! + 1434*x^7/7! + ...

where

log(A(x)) = x^2/2 + x^3/3 + x^5/5 + x^7/7 + x^11/11 + x^13/13 + x^17/17 + x^19/19 + x^23/23 + x^29/29 + ... + x^prime(n)/prime(n) + ...

a(5) = 44 because there are 5!/5 = 24 permutations that are 5-cycles and there are 5!/(2*3) = 20 permutations that are the disjoint product of a 2-cycle and a 3-cycle. - Geoffrey Critzer, Nov 08 2015

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(`if`(isprime(j),

      a(n-j)*(j-1)!*binomial(n-1, j-1), 0), j=1..n))

    end:

seq(a(n), n=0..25);  # Alois P. Heinz, May 12 2016

MATHEMATICA

f[list_] :=Total[list]!/Apply[Times, list]/Apply[Times, Map[Length, Split[list]]!]; Table[Total[Map[f, Select[Partitions[n], Apply[And, PrimeQ[#]] &]]], {n, 0, 23}] (* Geoffrey Critzer, Nov 08 2015 *)

PROG

(PARI) {a(n)=n!*polcoeff(exp(sum(k=1, n, x^prime(k)/prime(k))+x*O(x^n)), n)}

for(n=0, 31, print1(a(n), ", "))

CROSSREFS

Cf. A000040, A214003, A273001, A273998, A317131.

Sequence in context: A100015 A317672 A042819 * A255969 A239850 A100443

Adjacent sequences:  A217999 A218000 A218001 * A218003 A218004 A218005

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 17 2012

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 September 16 06:21 EDT 2019. Contains 327090 sequences. (Running on oeis4.)