A063715 Number of solutions (r,u,s,t) in positive integers to the system of equations 1/r + 1/u = 1/n, 1/s + 1/t = 1/u.

3, 17, 29, 49, 45, 111, 37, 115, 109, 159, 69, 319, 45, 207, 279, 191, 69, 367, 69, 487, 315, 183, 93, 681, 141, 235, 291, 495, 117, 909, 53, 357, 331, 259, 559, 967, 45, 279, 459, 949, 117, 1025, 69, 663, 815, 219, 117, 1205, 161, 591, 411, 555, 93, 965, 579

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Formula

a(n) = Sum_{d|n^2} tau((n+d)^2).

Example

For n=2 we have 17 solutions (r,u,s,t): (3,6,7,42), (3,6,8,24), (3,6,9,18), (3,6,10,15), (3,6,12,12), (3,6,15,10), (3,6,18,9), (3,6,24,8), (3,6,42,7), (4,4,5,20), (4,4,6,12), (4,4,8,8), (4,4,12,6), (4,4,20,5), (6,3,4,12), (6,3,6,6), (6,3,12,4).

Prog

(PARI) a(n) = sumdiv(n^2, d, numdiv((n+d)^2)) \\ Michel Marcus, Jun 17 2013

Crossrefs

Cf. A000005, A048691, A063716, A048691, A004194, A063520.

Sequence in context: A007490 A173587 A022887 * A105411 A107158 A188620

Adjacent sequences: A063712 A063713 A063714 * A063716 A063717 A063718

Keyword

nonn

Author

Vladeta Jovovic, Aug 10 2001

Status

approved