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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211996 Number of ordered pairs (i,j) such that i*j=n and i+j is a square. 3
0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)=1 for n>0 in A141046.

a(8820)=8 and it is the only term in the first 10000 terms that is greater than 6. There are 977 terms in the first 10000 terms that are greater than zero. - Harvey P. Dale, Nov 08 2012

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. Clark, An arithmetical function associated with the rank of elliptic curves, Canad. Math. Bull. Vol. 34 (2), 1991 pp. 181-185.

EXAMPLE

For n=3, the pairs (a,b) such that a*b=3 are (1,3) and (3,1). Both pairs add up to a square, so a(3) = 2.

MATHEMATICA

nop[n_]:=Module[{divs=Divisors[n]}, Count[Thread[{divs, Reverse[divs]}], _?(IntegerQ[Sqrt[Total[#]]]&)]]; Array[nop, 90] (* Harvey P. Dale, Nov 08 2012 *)

PROG

(PARI) a(n) = {for (i=1, n, nb = 0; fordiv(i, d, if (issquare(d+i/d), nb++)); print1(nb, ", "); ); }

(Haskell)

a211996 n = length [x | x <- [1..n], let (y, m) = divMod n x,

                        m == 0, a010052 (x + y) == 1]

-- Reinhard Zumkeller, Oct 28 2012

CROSSREFS

Cf. A010052.

Sequence in context: A127841 A091006 A167365 * A227834 A025894 A051127

Adjacent sequences:  A211993 A211994 A211995 * A211997 A211998 A211999

KEYWORD

nonn

AUTHOR

Michel Marcus, Oct 25 2012

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 November 13 07:13 EST 2019. Contains 329085 sequences. (Running on oeis4.)