A110157 a(n) = a(rad(n) - 1) + 1, where rad(n) is the squarefree kernel of n, rad=A007947.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Jul 14 2005

Keywords

• nonn

Comments

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

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Programs

Haskell

a110157 n = genericIndex a110157_list (n-1)
a110157_list = 0 : map ((+ 1) . a110157 . (+ 1)) a075423_list
-- Reinhard Zumkeller, Aug 14 2013

PARI

rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])
a(n)=if(n<4,n,1+a(rad(n)-1)) \\ Charles R Greathouse IV, Aug 08 2013

Formula

a(n) < 4 log_2(n) for n > 1. - Charles R Greathouse IV, Aug 08 2013