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A128651 In the sequence of natural numbers, replace the nonsquarefree numbers with their minimal factorization into squarefree numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)