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A050985
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Cubefree part of n.
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21
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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;
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internal format)
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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Dirichlet g.f.: zeta(3s)*zeta(s-1)/zeta(3s-3). - R. J. Mathar, Feb 11 2011
Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / (1890*Zeta(3)). - Vaclav Kotesovec, Feb 08 2019
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MAPLE
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end proc:
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MATHEMATICA
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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 *)
f[p_, e_] := p^Mod[e, 3]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *)
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PROG
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(Python)
from operator import mul
from functools import reduce
from sympy import factorint
return 1 if n <=1 else reduce(mul, [p**(e % 3) for p, e in factorint(n).items()])
(PARI) a(n) = my(f=factor(n)); f[, 2] = apply(x->(x % 3), f[, 2]); factorback(f); \\ Michel Marcus, Jan 06 2019
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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