A110157 - OEIS

%I #11 Aug 14 2013 19:12:58

%S 0,1,2,3,2,3,4,5,2,3,4,5,4,5,6,7,2,3,4,5,4,5,6,7,4,3,4,3,6,7,8,9,2,3,

%T 4,5,4,5,6,7,4,5,6,7,6,7,8,9,4,5,4,5,4,5,4,5,6,7,8,9,8,9,10,5,2,3,4,5,

%U 4,5,6,7,4,5,6,7,6,7,8,9,4,3,4,5,6,7,8,9,6,7,8,9,8,9,10,11,4,5,6,3,4,5,6,7

%N a(n) = a(rad(n) - 1) + 1, where rad(n) is the squarefree kernel of n, rad=A007947.

%C a(n) = a(A075423(n)) + 1;

%C a(A075426(n)) = n+1 and a(m) < n+1 for m < A075426(n).

%H Reinhard Zumkeller, <a href="/A110157/b110157.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) < 4 log_2(n) for n > 1. - _Charles R Greathouse IV_, Aug 08 2013

%o (PARI) rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])

%o a(n)=if(n<4,n,1+a(rad(n)-1)) \\ _Charles R Greathouse IV_, Aug 08 2013

%o (Haskell)

%o a110157 n = genericIndex a110157_list (n-1)

%o a110157_list = 0 : map ((+ 1) . a110157 . (+ 1)) a075423_list

%o -- _Reinhard Zumkeller_, Aug 14 2013

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Jul 14 2005