%I A160691
%S A160691 1,2,2,2,4,2,2,4,2,2,4,2,2,4,2,4,2,4,4,4,2,4,4,4,2,4,6,4,6,2,4,4,4,4,4,
%T A160691 4,4,4,4,4,4,2,2,4,4,4,2,4,4,2,4,2,4,4,4,2,2,4,4,2,4,4,4,2,4,2,4,4,2,4,
%U A160691 4,4,4,4,4,4,4,4,4,4,4,2,2,4,2,4,4,2,4,4,4,4,4,4,4,4,2,4,2,4,4,2,4,4,2
%N A160691 a(n) = the number of divisors of A160689(n) = the number of divisors 
               of A160690(n).
%C A160691 Contribution from Farideh Firoozbakht (mymontain(AT)yahoo.com), May 28 
               2009: (Start)
%C A160691 For the first 200000 natural numbers n, a(n) is in the set {1,2,4,6,8,
               12}
%C A160691 and in fact we have:
%C A160691 For one number n, A160691(n)=1.
%C A160691 For 13 numbers n, A160691(n)=12 (see the sequence A158963).
%C A160691 For 4785 numbers n, A160691(n)=6.
%C A160691 For 6706 numbers n, A160691(n)=8.
%C A160691 For 26790 numbers n, A160691(n)=2.
%C A160691 For 161705 numbers n, A160691(n)=4.
%C A160691 Also n=2 is the only number n (less than 200000) that a(n)=a(n+1)=a(n+2)=2.
%C A160691 and for the 53 consecutive numbers 64833, 64834, ... , 64885 we have 
               a(n)=4. (End)
%t A160691 Contribution from Farideh Firoozbakht (mymontain(AT)yahoo.com), May 28 
               2009: (Start)
%t A160691 c[1]=1;c[n_]:=c[n]=(s=Sum[c[k],{k,n-1}];For[m=1,DivisorSigma[0,m]!=
%t A160691 DivisorSigma[0,s+m],m++ ];m);a[n_]:=a[n]=DivisorSigma[0,c[n]];
%t A160691 Table[a[n],{n,105}] (End)
%Y A160691 A160689, A160690
%Y A160691 Cf. A158963, A158964. [From Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               May 28 2009]
%Y A160691 Sequence in context: A075016 A102445 A027389 this_sequence A049716 A066671 
               A159802
%Y A160691 Adjacent sequences: A160688 A160689 A160690 this_sequence A160692 A160693 
               A160694
%K A160691 nonn
%O A160691 1,2
%A A160691 Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), May 24 2009
%E A160691 More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), May 28 
               2009