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A063716 Number of solutions (r,u,s,t), s>=t, in positive integers to the system of equations 1/r+1/u=1/n, 1/s+1/t=1/u. 1
2, 10, 16, 27, 24, 60, 20, 61, 57, 84, 36, 167, 24, 108, 144, 100, 36, 191, 36, 251, 162, 96, 48, 351, 73, 122, 149, 255, 60, 468, 28, 184, 170, 134, 284, 496, 24, 144, 234, 485, 60, 526, 36, 339, 415, 114, 60, 616, 83, 303, 210, 285, 48, 493, 294, 585, 210, 144, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278.  Solution published in Vol. 38, No. 2, May 2000, pp. 183-184.

LINKS

Table of n, a(n) for n=1..59.

FORMULA

a(n) = (tau(n^2) + Sum_{d|n^2} tau((n+d)^2))/2 = (A048691(n)+A063715(n))/2.

EXAMPLE

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

CROSSREFS

Cf. A000005, A048691, A063715, A018892, A048691, A004194, A063520.

Sequence in context: A060658 A239321 A054028 * A125212 A341060 A189329

Adjacent sequences:  A063713 A063714 A063715 * A063717 A063718 A063719

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Aug 10 2001

STATUS

approved

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Last modified June 13 17:14 EDT 2021. Contains 345008 sequences. (Running on oeis4.)