The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A050985 Cubefree part of n. 15
 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 Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale) Henry 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 Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / (1890*Zeta(3)). - Vaclav Kotesovec, Feb 08 2019 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[]- Mod[ tr[], 3]; cb=Times@@(First[#]^Last[#]&/@Transpose[{tr[], ex}]); n/cb]; Array[cf, 75] (* Harvey P. Dale, Jun 03 2012 *) f[p_, e_] := p^Mod[e, 3]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *) 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 (PARI) a(n) = my(f=factor(n)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)