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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318360 Number of set multipartitions (multisets of sets) of a multiset whose multiplicities are the prime indices of n. 23
1, 1, 1, 2, 1, 2, 1, 5, 3, 2, 1, 6, 1, 2, 3, 15, 1, 9, 1, 6, 3, 2, 1, 21, 4, 2, 16, 6, 1, 10, 1, 52, 3, 2, 4, 35, 1, 2, 3, 22, 1, 10, 1, 6, 19, 2, 1, 83, 5, 13, 3, 6, 1, 66, 4, 22, 3, 2, 1, 41, 1, 2, 20, 203, 4, 10, 1, 6, 3, 14, 1, 153, 1, 2, 26, 6, 5, 10, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A050320(A181821(n)).

From Andrew Howroyd, Dec 10 2018:(Start)

a(p) = 1 for prime(p).

a(prime(i)*prime(j)) = min(i,j) + 1.

a(prime(n)^k) = A188392(n,k). (End)

EXAMPLE

The a(12) = 6 set multipartitions of {1,1,2,3}:

  {{1},{1,2,3}}

  {{1,2},{1,3}}

  {{1},{1},{2,3}}

  {{1},{2},{1,3}}

  {{1},{3},{1,2}}

  {{1},{1},{2},{3}}

MATHEMATICA

nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];

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

Table[Length[sqfacs[Times@@Prime/@nrmptn[n]]], {n, 80}]

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

sig(n)={my(f=factor(n)); concat(vector(#f~, i, vector(f[i, 2], j, primepi(f[i, 1]))))}

count(sig)={my(n=vecsum(sig), s=0); forpart(p=n, my(q=prod(i=1, #p, 1 + x^p[i] + O(x*x^n))); s+=prod(i=1, #sig, polcoef(q, sig[i]))*permcount(p)); s/n!}

a(n)={if(n==1, 1, my(s=sig(n)); if(#s<=2, if(#s==1, 1, min(s[1], s[2])+1), count(sig(n))))} \\ Andrew Howroyd, Dec 10 2018

CROSSREFS

Cf. A001055, A007716, A049311, A116540, A181821, A188392, A255906.

Cf. A318283, A318284, A318286, A318361, A318362, A318369.

Sequence in context: A146002 A109087 A102048 * A102551 A217437 A152823

Adjacent sequences:  A318357 A318358 A318359 * A318361 A318362 A318363

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 24 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 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)