login
a(1) = 1, for n > 1: a(n) = tau(sum of the previous terms) where tau(k) = number of the divisors of k.
2

%I #5 Mar 29 2014 18:26:37

%S 1,1,2,3,2,3,6,6,8,6,4,8,6,8,7,2,2,6,5,4,12,8,8,4,4,12,8,4,12,10,6,4,

%T 8,8,12,16,4,8,8,8,4,8,8,4,4,8,8,4,4,12,8,4,16,4,12,4,8,8,4,4,16,8,12,

%U 8,8,8,18,18,12,8,8,4,8,4,8,4,4,16,4,4,16,4,8,8,8,4,8,4,24,8,4,12,8,8,4,4,16

%N a(1) = 1, for n > 1: a(n) = tau(sum of the previous terms) where tau(k) = number of the divisors of k.

%C a(1) = 1, for n > 1: a(n) = tau(sum_(i=1...n-1) a(i)) = A000005(sum_(i=1...n-1) a(i)). a(n) = inverse of partial sums of A064491(n), i.e. a(1) = A064491(1), for n > 1: a(n) = A064491(n) - A064491(n-1), i.e. first differences of sequence A064491.

%H Reinhard Zumkeller, <a href="/A165930/b165930.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = tau(a(1)+a(2)+a(3)) = tau(4) = 3.

%o (PARI) print1(1);s=1;for(n=2,1e4,a=numdiv(s);print1(","a);s+=a)

%o (Haskell)

%o a165930 n = a165930_list !! (n-1)

%o a165930_list = 1 : zipWith (-) (tail a064491_list) a064491_list

%o -- _Reinhard Zumkeller_, Mar 29 2014

%K nonn

%O 1,3

%A _Jaroslav Krizek_, Sep 30 2009

%E Program and editing by _Charles R Greathouse IV_, Nov 02 2009