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

1,3

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A237513 A137844 A263845 * A344972 A204988 A368332

Adjacent sequences: A079226 A079227 A079228 * A079230 A079231 A079232

Keyword

nonn

Author

Reinhard Zumkeller, Jan 02 2003

Status

approved