%I A121382
%S A121382 1,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,3,1,2,1,2,1,5,1,1,2,2,2,
%T A121382 2,1,2,2,2,1,5,1,2,2,2,1,3,1,2,2,2,1,2,2,2,2,2,1,7,1,2,2,1,2,5,1,2,2,5,
%U A121382 1,2,1,2,2,2,2,5,1,3,1,2,1,6,2,2,2,2,1,6,2,2,2,2,2,3,1,2,2,2,1,5,1,2,5
%N A121382 Number of ways of writing n as pqr, with p<=q<=r and (p,q)=(q,r)=1.
%C A121382 3-factor analogue of A007875 Number of ways of writing n as pq, with 
               p<=q, (p,q)=1.
%C A121382 a(n) = 1 iff n is a power prime (A000961).
%e A121382 a(4) = 1 because 4 = 1*1*4.
%e A121382 a(6) = 2 because 6 = 1*1*6 = 1*2*3.
%e A121382 a(24) = 3 because 24 = 1*1*24 = 1*3*8 = 2*3*4.
%e A121382 a(30) = 5 because 30 = 1*1*30 = 1*2*15 = 1*3*10 = 1*5*6 = 2*3*5.
%t A121382 f[n_] := Block[{d = Divisors@n, m = DivisorSigma[0, n], s = {}}, If[m 
               == 2, 1, Do[ AppendTo[s, {d[[p]], d[[q]], d[[r]]}], {r, m}, {q, r}, 
               {p, q}]; Length@ Select[s, Times @@ # == n && GCD[ #[[1]], #[[2]]] 
               == GCD[ #[[2]], #[[3]]] == 1 &]]]; Array[f, 105] (* Robert G. Wilson 
               v *)
%Y A121382 Cf. A000040, A001248, A001358, A007304, A007875, A030078.
%Y A121382 First occurrence of k: A122829.
%Y A121382 Sequence in context: A096825 A007875 A050320 this_sequence A051265 A008647 
               A036475
%Y A121382 Adjacent sequences: A121379 A121380 A121381 this_sequence A121383 A121384 
               A121385
%K A121382 easy,nonn
%O A121382 1,6
%A A121382 Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 06 2006
%E A121382 Edited, corrected and extended by Robert G. Wilson v Sep 11 2006