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!)
A079275 Number of divisors of n that are semiprimes with distinct factors. 6
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 3, 0, 1, 1, 0, 1, 3, 0, 1, 1, 3, 0, 1, 0, 1, 1, 1, 1, 3, 0, 1, 0, 1, 0, 3, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,30

COMMENTS

Number of pairs of prime factors of n, (p,q), such that p < q. For example, the prime factors of 30 are 2, 3 and 5, so we have the ordered pairs (2,3), (2,5) and (3,5). - Wesley Ivan Hurt, Sep 14 2020

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

a(A000961(n)) = 0; a(A007774(n)) = 1; a(A033992(n)) = 3; a(A033993(n)) = 6.

a(n) = omega(n)*(omega(n)-1)/2, where omega(n) is the number of distinct prime factors of n.

a(n) = Sum_{p|n, q|n, p,q prime, p<q} 1. - Wesley Ivan Hurt, Sep 14 2020

MAPLE

A079275 := proc(n)

    local a, d ;

    a := 0 ;

    for d in numtheory[divisors](n) do

        if A001221(d) = 2 and A001222(d) = 2 then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc:

seq(A079275(n), n=1..40) ; # R. J. Mathar, Jan 18 2021

MATHEMATICA

f[n_]:=Module[{c=PrimeNu[n]}, (c(c-1))/2]; Array[f, 110] (* Harvey P. Dale, Oct 05 2011 *)

PROG

(PARI) a(n) = sumdiv(n, d, (bigomega(d)==2) && (omega(d)==2)); \\ Michel Marcus, Sep 15 2020

(PARI) a(n) = binomial(omega(n), 2) \\ David A. Corneth, Sep 15 2020

CROSSREFS

Cf. A000005, A000961, A001221, A001358, A006881, A007774, A033992, A033993.

Sequence in context: A318508 A100655 A262262 * A236314 A236322 A319419

Adjacent sequences:  A079272 A079273 A079274 * A079276 A079277 A079278

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Feb 07 2003

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 August 3 19:49 EDT 2021. Contains 346441 sequences. (Running on oeis4.)