A079229 Least k>0 such that rad(n+k) > rad(n), where rad is the squarefree kernel (A007947).

1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Jan 02 2003

Keywords

• nonn

Comments

A020754 probably gives the records in this sequence. - Charles R Greathouse IV, Aug 02 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

a(n) = A079228(n) - n.

Programs

Haskell

a079229 n = a079229_list !! (n-1)
a079229_list = f a007947_list where
   f (x:xs) = ((+ 1) . length $ takeWhile (<= x) xs) : f xs
-- Reinhard Zumkeller, Oct 06 2012

Mathematica

rad[n_] := Times @@ FactorInteger[n][[All, 1]]; a[1] = 1; a[n_] := For[k = 1, True, k++, If[ rad[n+k] > rad[n], Return[k]]]; Table[ a[n], {n, 1, 105}] (* Jean-François Alcover, Oct 05 2012 *)

PARI

rad(n)=my(f=factor(n)[,1]);prod(i=1,#f,f[i])
a(n)=my(r=rad(n),k);while(r>=rad(n+k++),);k \\ Charles R Greathouse IV, Aug 02 2013