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!)
A140773 Consider the products of all pairs of (not necessarily distinct) positive divisors of n. a(n) = the number of these products that divide n. a(n) also = the number of the products that are divisible by n. 2
1, 2, 2, 4, 2, 5, 2, 6, 4, 5, 2, 10, 2, 5, 5, 9, 2, 10, 2, 10, 5, 5, 2, 16, 4, 5, 6, 10, 2, 14, 2, 12, 5, 5, 5, 20, 2, 5, 5, 16, 2, 14, 2, 10, 10, 5, 2, 24, 4, 10, 5, 10, 2, 16, 5, 16, 5, 5, 2, 28, 2, 5, 10, 16, 5, 14, 2, 10, 5, 14, 2, 32, 2, 5, 10, 10, 5, 14, 2, 24, 9, 5, 2, 28, 5, 5, 5, 16, 2, 28, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

EXAMPLE

The divisors of 20 are 1,2,4,5,10,20. There are 10 pairs of divisors whose product divides 20: 1*1=1, 1*2=2, 1*4=4, 1*5=5, 1*10=10, 1*20=20, 2*2=4, 2*5=10, 2*10=20, 4*5 = 20. Likewise, there are 10 products that are divisible by 20: 4*5=20, 2*10=20, 4*10=40, 10*10=100, 1*20=20, 2*20=40, 4*20=80, 5*20=100, 10*20=200, 20*20=400. So a(20) = 10.

MATHEMATICA

(* first do *) Needs["Combinatorica`"] (* then *) f[n_] := Count[ n/Times @@@ Union[Sort /@ Tuples[Divisors@ n, 2]], _Integer]; Array[f, 91] - Robert G. Wilson v, May 31 2008

PROG

(PARI)

\\ Two implementations, after the two different interpretations given by the author of the sequence:

A140773v1(n) = { my(ds = divisors(n), s=0); for(i=1, #ds, for(j=i, #ds, if(!(n%(ds[i]*ds[j])), s=s+1))); s; }

A140773v2(n) = { my(ds = divisors(n), s=0); for(i=1, #ds, for(j=i, #ds, if(!((ds[i]*ds[j])%n), s=s+1))); s; }

\\ Antti Karttunen, May 19 2017

CROSSREFS

Cf. A140774.

Sequence in context: A054134 A319822 A005127 * A133911 A069932 A056148

Adjacent sequences:  A140770 A140771 A140772 * A140774 A140775 A140776

KEYWORD

nonn

AUTHOR

Leroy Quet, May 29 2008

EXTENSIONS

Corrected and extended by Robert G. Wilson v, May 31 2008

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 September 18 20:19 EDT 2020. Contains 337173 sequences. (Running on oeis4.)