%I A086435
%S A086435 0,1,1,1,1,2,1,2,1,2,1,2,1,2,2,2,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,2,
%T A086435 3,1,2,2,3,1,3,1,2,2,2,1,3,1,2,2,2,1,3,2,3,2,2,1,3,1,2,2,3,2,3,1,2,2,3,
%U A086435 1,3,1,2,2,2,2,3,1,3,2,2,1,3,2,2,2,3,1,3,2,2,2,2,2,3,1,2,2,3,1,3
%N A086435 Maximum number of parts possible in a factorization of n into a product 
               of distinct numbers > 1.
%C A086435 For n>1, a((n+1)!) = n is the first occurrence of n in the sequence. 
               This function depends only on the prime signature of n. - Franklin 
               T. Adams-Watters (FrankTAW(AT)Netscape.net), Dec 19 2006
%H A086435 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               UnorderedFactorization.html">UnorderedFactorization</a>
%e A086435 a(6)=2 since 6 may be factored into distinct parts as {{2,3},{6}}, so 
               the largest number of factors possible is 2.
%e A086435 a(8)=2 since 8 may be factored into distinct parts as {{8},{2,4}}, so 
               the largest numbers of factors possible is 2.
%o A086435 (PARI) { a(n,m=1) = if(n>m, 1 + vecmax( apply( x->if(x>m,a(n/x,x)), divisors(n) 
               ))) } [From Max Alekseyev (maxale(AT)gmail.com), Jul 16 2009]
%Y A086435 Cf. A000142, A025487.
%Y A086435 Sequence in context: A065031 A058061 A064547 this_sequence A099305 A033109 
               A111627
%Y A086435 Adjacent sequences: A086432 A086433 A086434 this_sequence A086436 A086437 
               A086438
%K A086435 nonn
%O A086435 1,6
%A A086435 Eric Weisstein (eric(AT)weisstein.com), Jul 19, 2003