| 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 1, 17, 6, 19, 10, 21, 22, 23, 6, 5, 26, 3, 14, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 3, 7, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 2, 65, 66, 67, 34, 69, 70, 71, 6, 73, 74, 15, 38
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If n=Product[Pj^Ej] then a(n)=Product[Pj^Fj], where Fj=0 if Ej is 0 or a multiple of 4, and Fj=1 otherwise
Multiplicative with a(p^e) = p^(if 4|e, then 0, else 1). - Mitch Harris, Apr 19 2005.
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LINKS
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H. Bottomley, Some Smarandache-type multiplicative sequences
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FORMULA
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a(n) =A007947(A053165(n)) =A053166(A053165(n)) =n/(A053164(n)*A000190(n)) =A053166(n)/A053164(n) =A056553(n)^(1/3)
Multiplicative with a(p^e) = p^(if 4|e, then 0, else 1).
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EXAMPLE
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a(64)=2 because 4-th-power-free part of 64 is 4 and power-free kernel of 4 is 2.
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CROSSREFS
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Cf. A000190, A007947, A008835, A053164, A053165, A053166, A053167, A056552, A056553, A056555.
Adjacent sequences: A056551 A056552 A056553 this_sequence A056555 A056556 A056557
Sequence in context: A049273 A053590 A086297 this_sequence A088835 A007947 A015053
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KEYWORD
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nonn,mult
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 25 2000
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