

A050985


Cubefree part of n.


11



1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 3, 25, 26, 1, 28, 29, 30, 31, 4, 33, 34, 35, 36, 37, 38, 39, 5, 41, 42, 43, 44, 45, 46, 47, 6, 49, 50, 51, 52, 53, 2, 55, 7, 57, 58, 59, 60, 61, 62, 63, 1, 65, 66, 67, 68, 69, 70, 71, 9, 73, 74, 75
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OFFSET

1,2


COMMENTS

This is an unusual sequence in the sense that the 83.2% of the integers that belong to A004709 occur infinitely many times, whereas the remaining 16.8% of the integers that belong to A046099 never occur at all.  Ant King, Sep 22 2013


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
H. Bottomley, Some Smarandachetype multiplicative sequences
Eric Weisstein's World of Mathematics, Cubefree part.


FORMULA

Multiplicative with p^e > p^(e mod 3), p prime. [Reinhard Zumkeller, Nov 22 2009]
Dirichlet g.f. zeta(3s)*zeta(s1)/zeta(3s3).  R. J. Mathar, Feb 11 2011


MATHEMATICA

cf[n_]:=Module[{tr=Transpose[FactorInteger[n]], ex, cb}, ex= tr[[2]] Mod[ tr[[2]], 3]; cb=Times@@(First[#]^Last[#]&/@Transpose[{tr[[1]], ex}]); n/cb]; Array[cf, 75] (* Harvey P. Dale, Jun 03 2012 *)


CROSSREFS

Cf. A007913, A008834, A053165, A004709, A046099.
Sequence in context: A033928 A194754 A167972 * A056192 A030107 A037895
Adjacent sequences: A050982 A050983 A050984 * A050986 A050987 A050988


KEYWORD

nonn,easy,mult


AUTHOR

Eric W. Weisstein


STATUS

approved



