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

%I

%S 1,0,1,2,3,44,55,1434,3913,39752,392481,5109290,34683451,914698212,

%T 5777487703,91494090674,1504751645265,31764834185744,379862450767873,

%U 12634073744624082,132945783064464691,2753044719709341980,64135578414076991031,1822831113987975441482

%N E.g.f.: exp( Sum_{n>=1} x^prime(n) / prime(n) ).

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

%C 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

%H Alois P. Heinz, <a href="/A218002/b218002.txt">Table of n, a(n) for n = 0..450</a>

%e 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! + ...

%e where

%e 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) + ...

%e 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

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

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

%p end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, May 12 2016

%t 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 *)

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

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

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

%K nonn

%O 0,4

%A _Paul D. Hanna_, Oct 17 2012

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 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)