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

Author

Reinhard Zumkeller, Mar 18 2007

Keywords

• nonn

Comments

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

Examples

			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 ....
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Squarefree

Crossrefs

Cf. A013929, A007947, A003557.

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).