A168324 Number of distinct permutations of the list of prime factors of n (with multiplicity), where a(1)=0.

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 6, 1, 1, 2, 2, 2, 6, 1, 2, 2, 4, 1, 6, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 12, 1, 2, 3, 1, 2, 6, 1, 3, 2, 6, 1, 10, 1, 2, 3, 3, 2, 6, 1, 5, 1, 2, 1, 12, 2, 2, 2, 4, 1, 12, 2, 3, 2, 2, 2, 6, 1, 3, 3, 6, 1, 6, 1, 4, 6

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 22 2009, May 08 2010

Keywords

• nonn

Comments

Apart from a(1) the same as A008480.

Examples

			a(18)=3 because 18=2*2*3=2*3*2=3*2*2;
a(24)=4 because 24=2*2*2*3=2*2*3*2=2*3*2*2=3*2*2*2;
a(26)=2 because 26=2*13=13*2;
a(30)=6 because 30=2*3*5=2*5*3=3*2*5=3*5*2=5*2*3=5*3*2.
		

Crossrefs

Cf. A066882, A008480 (same except for initial term).

Programs

Mathematica

nn = 105;
f[list_, i] := list[[i]];
a =Table[Boole[PrimeQ[n]], {n, 1, nn}]; Map[Total,Transpose[NestList[Table[
DirichletConvolve[f[#, n], f[a, n], n, m], {m, 1, nn}] &, a,nn]]] (* Geoffrey Critzer, Feb 16 2015 *)

Extensions

Entries checked by D. S. McNeil, Nov 26 2010