A177962 Number of distinct transpositions of prime factors of n-th composite number.

1, 2, 1, 1, 2, 3, 2, 2, 1, 3, 3, 2, 2, 4, 1, 2, 1, 3, 6, 1, 2, 2, 2, 6, 2, 2, 4, 6, 3, 3, 2, 5, 1, 3, 2, 3, 4, 2, 4, 2, 2, 12, 2, 3, 1, 2, 6, 3, 2, 6, 10, 2, 3, 3, 2, 6, 5, 1, 2, 12, 2, 2, 2, 4, 12, 2, 3, 2, 2, 2, 6, 3, 3, 6, 6, 4, 6, 2, 10, 6, 2, 5, 6, 2, 3, 3, 2, 2, 20, 1, 2, 2, 3, 1, 12, 1, 2, 6, 12, 2, 2

Offset: 1

Author

Juri-Stepan Gerasimov, May 16 2010

Keywords

• nonn

Examples

			a(1)=1 because 1st composite = 4 and (2*2)=1.
a(2)=2 because 2nd composite = 6 and (2*3 or 3*2) = 2.
		

Crossrefs

Cf. A002808, A177687.

Programs

Maple

A177962 := proc(n) local c; c := A002808(n) ; a := (numtheory[bigomega](c))! ; for p in ifactors(c)[2] do a := a/ op(2,p)! ; end do: a ; end proc:
seq(A177962(n),n=1..120) ; # R. J. Mathar, May 28 2010

Formula

a(n) = A008480(A002808(n)). - R. J. Mathar, May 28 2010

Extensions

Entries checked by R. J. Mathar, May 28 2010