

A050985


Cubefree part of n.


12



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
Eric Weisstein's World of Mathematics, Dirichlet Generating Function


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
a(n) = n/A008834(n).  R. J. Mathar, Dec 08 2015


MAPLE

A050985 := proc(n)
n/A008834(n) ;
end proc:
seq(A050985(n), n=1..40) ; # R. J. Mathar, Dec 08 2015


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 *)


PROG

(Python)
from operator import mul
from functools import reduce
from sympy import factorint
def A050985(n):
....return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(n).items()])
# Chai Wah Wu, Feb 04 2015


CROSSREFS

Cf. A007913, A008834, A053165, A004709, A046099.
Sequence in context: A033928 A194754 A167972 * A270418 A056192 A255693
Adjacent sequences: A050982 A050983 A050984 * A050986 A050987 A050988


KEYWORD

nonn,easy,mult


AUTHOR

Eric W. Weisstein, Dec 11 1999


STATUS

approved



