

A204455


Squarefree product of all odd primes dividing n, and 1 if n is a power of 2: A099985/2.


14



1, 1, 3, 1, 5, 3, 7, 1, 3, 5, 11, 3, 13, 7, 15, 1, 17, 3, 19, 5, 21, 11, 23, 3, 5, 13, 3, 7, 29, 15, 31, 1, 33, 17, 35, 3, 37, 19, 39, 5, 41, 21, 43, 11, 15, 23, 47, 3, 7, 5, 51, 13, 53, 3, 55, 7, 57, 29, 59, 15, 61, 31, 21, 1, 65, 33, 67, 17, 69, 35, 71, 3
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OFFSET

1,3


COMMENTS

There are no odd primes dividing n iff n is a power of 2.
This sequence coincides with the bisection of A007947 (even indices), which is A099985, dividing out the even prime 2 in the squarefree kernel.
a(n) divides A106609(n) for n>=1.  Alexander R. Povolotsky, Apr 06 2015


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A099985(n)/2 = A007947(2*n)/2.
a(n) = A000265(A007947(n)) = A007947(A000265(n)).  Charles R Greathouse IV, Jan 19 2012
Multiplicative with a(p^e)=p for p <> 2 and a(2^e)=1.  R. J. Mathar, Jul 02 2013
a(n) = Sum_{dn} phi(d)*mu(2d)^2.  Ridouane Oudra, Sep 02 2019


EXAMPLE

a(5)=5 because 5 is a single odd prime.
a(9)=3 because 9=3*3 has as squarefree part 3.
a(1)=1 because 1 is a power of 2, having no odd primes as a factor.


MAPLE

A204455 := proc(n)
local p;
numtheory[factorset](n) minus {2} ;
mul(p, p=%) ;
end proc:
seq(A204455(n), n=1..40) ; # R. J. Mathar, Jan 25 2017


MATHEMATICA

f[n_] := Select[First /@ FactorInteger@ n, PrimeQ@ # && OddQ@ # &]; Times @@@ (f /@ Range@ 120) (* Michael De Vlieger, Apr 08 2015 *)


PROG

(PARI) a(n) = {my(f = factor(n)); prod(k=1, #f~, if (f[k, 1] % 2, f[k, 1], 1)); } \\ Michel Marcus, Apr 07 2015


CROSSREFS

Cf. A099985, A099984, A007947, A000265, A106609.
Sequence in context: A078701 A299766 A161398 * A318653 A161820 A116528
Adjacent sequences: A204452 A204453 A204454 * A204456 A204457 A204458


KEYWORD

nonn,mult


AUTHOR

Wolfdieter Lang, Jan 19 2012


STATUS

approved



