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Search: id:A128651
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| A128651 |
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In the sequence of natural numbers, replace the non-square-free numbers by their minimal factorization into square-free numbers. |
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+0
4
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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a(A129132(n-1) + 2) = A007947(n) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 30 2007
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Squarefree
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FORMULA
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a(n) = f(n,1,2,2,1) with f(n,m,x,y,z) = if n=m then z else if sfk(y)=y then f(n,m+1,x+1,x+1,y) else f(n,m+1,x,y/sfk(y),sfk(y)), sfk = square-free kernel (A007947).
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EXAMPLE
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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 ....
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CROSSREFS
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Cf. A013929, A007947, A003557.
Sequence in context: A053269 A118665 A027746 this_sequence A093797 A119809 A007653
Adjacent sequences: A128648 A128649 A128650 this_sequence A128652 A128653 A128654
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 18 2007
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