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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 (list; graph; refs; listen; history; text; internal format)
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 Smarandache-type 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(s-1)/zeta(3s-3). - 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 *)

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 * A056192 A255693 A030107

Adjacent sequences:  A050982 A050983 A050984 * A050986 A050987 A050988

KEYWORD

nonn,easy,mult

AUTHOR

Eric W. Weisstein, Dec 11 1999

STATUS

approved

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Last modified April 27 22:06 EDT 2015. Contains 257094 sequences.