A128651 In the sequence of natural numbers, replace the nonsquarefree numbers with their minimal factorization into squarefree numbers.

1, 2, 3, 2, 2, 5, 6, 7, 2, 2, 2, 3, 3, 10, 11, 6, 2, 13, 14, 15, 2, 2, 2, 2, 17, 6, 3, 19, 10, 2, 21, 22, 23, 6, 2, 2, 5, 5, 26, 3, 3, 3, 14, 2, 29, 30, 31, 2, 2, 2, 2, 2, 33, 34, 35, 6, 6, 37, 38, 39, 10, 2, 2, 41, 42, 43, 22, 2, 15, 3, 46, 47, 6, 2, 2, 2, 7, 7, 10, 5, 51, 26, 2, 53, 6, 3, 3, 55

Offset

1,2

Comments

a(A129132(n-1) + 2) = A007947(n) for n > 1. - Reinhard Zumkeller, Mar 30 2007

Links

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

Eric Weisstein's World of Mathematics, Squarefree

Formula

a(n) = f(n,1,2,2,1) with f(n,m,x,y,z) = if n=m then z else if rad(y)=y then f(n,m+1,x+1,x+1,y) else f(n,m+1,x,y/rad(y),rad(y)), rad = squarefree kernel (A007947).

Example

1 2 3 _ 4 5 6 7 _ _ 8 _ 9 10 11 _12 13 14 15 _ _ _16 ....
1 2 3 2 2 5 6 7 2 2 2 3 3 10 11 6 2 13 14 15 2 2 2 2 ....

Crossrefs

Cf. A013929, A007947, A003557.

Sequence in context: A166454 A283239 A318177 * A093797 A214320 A119809

Adjacent sequences: A128648 A128649 A128650 * A128652 A128653 A128654

Keyword

nonn

Author

Reinhard Zumkeller, Mar 18 2007

Status

approved