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A056552
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Power-free kernel of cube-free part of n.
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6
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1, 2, 3, 2, 5, 6, 7, 1, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, 19, 10, 21, 22, 23, 3, 5, 26, 1, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 5, 41, 42, 43, 22, 15, 46, 47, 6, 7, 10, 51, 26, 53, 2, 55, 7, 57, 58, 59, 30, 61, 62, 21, 1, 65, 66, 67, 34, 69, 70, 71, 3, 73, 74, 15, 38, 77
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If n=Product[Pj^Ej] then a(n)=Product[Pj^Fj], where Fj=0 if Ej is 0 or a multiple of 3 and Fj=1 otherwise
Multiplicative with a(p^e) = p^(if 3|e, then 0, else 1). - Mitch Harris, Apr 19 2005.
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LINKS
| H. Bottomley, Some Smarandache-type multiplicative sequences
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FORMULA
| a(n) =A007947(A050985(n)) =A0195559(A050985(n)) =n/(A053150(n)*A000189(n)) =A019555(n)/A053150(n) =A056551(n)^(1/3)
Multiplicative with a(p^e) = p^(if 3|e, then 0, else 1).
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EXAMPLE
| a(32)=2 because cube-free part of 32 is 4 and power-free kernel of 4 is 2.
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CROSSREFS
| Cf. A000189, A000578, A007947, A008834, A019555, A048798, A050985, A053149, A053150, A056551.
Sequence in context: A088861 A088631 A086184 * A049273 A053590 A162323
Adjacent sequences: A056549 A056550 A056551 * A056553 A056554 A056555
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KEYWORD
| nonn,mult
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 25 2000
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