login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A273487 Density of numbers without prime exponents in their factorization. 1
6, 5, 0, 4, 4, 5, 6, 0, 8, 4, 2, 1, 9, 1, 2, 6, 9, 1, 3, 9, 0, 4, 4, 4, 3, 6, 1, 1, 0, 4, 6, 5, 9, 6, 4, 5, 5, 7, 7, 0, 1, 0, 2, 9, 6, 9, 2, 2, 0, 5, 4, 9, 7, 6, 0, 2, 0, 1, 9, 3, 5, 8, 8, 5, 5, 5, 2, 3, 4, 2, 8, 6, 9, 1, 6, 8, 2, 1, 3, 6, 7, 7, 4, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..84.

FORMULA

Prod_{p prime} 1 - (1 - 1/p)*Sum_{q prime} p^-q.

EXAMPLE

0.6504456084219126913904443611046...

MAPLE

eser := 1-x^2+x^4 ;

for pidx from 3 to 100 do

    p := ithprime(pidx) ;

    eser := eser -x^p+x^(p+1) ;

end do:

eser := taylor(eser, x=0, p) ;

gfun[seriestolist](eser) ;

subsop(1=NULL, %) ;

L := EULERi(%) ;

Digits := 180 ;

x := 1.0 ;

for i from 2 to nops(L) do

    if op(i, L) <> 0 then

        x := x*evalf(Zeta(i)^op(i, L)) ;

        printf("%.70f\n", x) ;

    fi ;

end do; # R. J. Mathar, Jul 11 2016

PROG

(PARI) leps=log(2)*(1-bitprecision(1.))

f(x)=my(s=0.); forprime(p=2, 1-leps/log(x), s+=x^-p); s

6/Pi^2*prodeuler(p=2, 1e6, (1-(1-1/p)*f(p))/(1-1/p^2))

CROSSREFS

Density of A274034.

Sequence in context: A010773 A099288 A256717 * A134103 A196621 A096434

Adjacent sequences:  A273484 A273485 A273486 * A273488 A273489 A273490

KEYWORD

nonn,cons

AUTHOR

Charles R Greathouse IV, Jul 01 2016

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 07:58 EDT 2020. Contains 335464 sequences. (Running on oeis4.)