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 A050985 Cubefree part of n. 14
 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 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, A301596, A301597. Sequence in context: A194754 A167972 A319656 * A270418 A056192 A255693 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 December 16 13:24 EST 2018. Contains 318167 sequences. (Running on oeis4.)