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%I #10 Feb 02 2015 11:04:18
%S 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,
%T 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,
%U 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
%N Number of distinct transpositions of prime factors of n-th composite number.
%F a(n) = A008480(A002808(n)). - _R. J. Mathar_, May 28 2010
%e a(1)=1 because 1st composite = 4 and (2*2)=1.
%e a(2)=2 because 2nd composite = 6 and (2*3 or 3*2) = 2.
%p 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:
%p seq(A177962(n),n=1..120) ; # _R. J. Mathar_, May 28 2010
%Y Cf. A002808, A177687.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, May 16 2010
%E Entries checked by _R. J. Mathar_, May 28 2010