login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323761 Denominator of Product_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k and tau(k) = the number of the divisors of k. 3
1, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 16, 15, 2, 1, 2, 9, 16, 2, 2, 1, 6, 2, 8, 9, 2, 8, 2, 45, 16, 2, 16, 1, 2, 2, 16, 9, 2, 8, 2, 9, 32, 2, 2, 25, 6, 9, 16, 9, 2, 1, 16, 9, 16, 2, 2, 1, 2, 2, 32, 315, 16, 8, 2, 9, 16, 8, 2, 1, 2, 2, 32, 9, 16, 8, 2, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.

LINKS

Table of n, a(n) for n=1..80.

FORMULA

a(p) = 2 for prime p > 2.

a(n) = 1 for numbers in A323762.

EXAMPLE

For n=4; Product_{d|4} (pod(d)/tau(d)) = (pod(1)/tau(1))*(pod(2)/tau(2))*(pod(4)/tau(4)) = (1/1)*(2/2)*(8/3) = 8/3; a(4) = 3.

MAPLE

A323761 := proc(n)

    denom(A266265(n)/A211776(n)) ;

end proc:

seq(A323761(n), n=1..20) ; # R. J. Mathar, Feb 13 2019

PROG

(MAGMA) [Denominator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]

(PARI) a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); denominator(p); \\ Michel Marcus, Jan 27 2019

CROSSREFS

Cf. A211776, A266265, A323760 (numerator), A323762.

Sequence in context: A208243 A209320 A097051 * A078832 A086410 A185049

Adjacent sequences:  A323758 A323759 A323760 * A323762 A323763 A323764

KEYWORD

nonn,frac

AUTHOR

Jaroslav Krizek, Jan 27 2019

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 June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)