|
Search: id:A063520
|
|
|
| A063520 |
|
Sum divides product: number of solutions (r,s,t), r>=s>=t>0, to the equation rst = n(r+s+t). |
|
+0
7
|
|
| 1, 3, 6, 5, 8, 8, 8, 14, 13, 9, 14, 17, 8, 18, 23, 18, 14, 17, 13, 33, 23, 10, 19, 36, 15, 22, 32, 22, 19, 26, 17, 39, 24, 18, 50, 45, 8, 22, 39, 38, 22, 27, 13, 50, 45, 16, 27, 52, 24, 39, 38, 27, 20, 50, 45, 72, 24, 12, 31, 58, 15, 28, 69, 45, 49, 39, 12, 52, 40, 33, 33, 66, 12, 33, 64
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Number of solutions (r,s) in positive integers to the equation rs = n(r+s) is tau(n^2), cf. A048691. Number of solutions (r,s), r>=s>0, to the equation rs = n(r+s) is (tau(n^2)+1)/2, cf. A018892.
Conjecturally, includes all positive integers except 2, 4, 7 and 11 - David W. Wilson (davidwwilson(AT)comcast.net)
|
|
REFERENCES
|
M. J. Pelling, "The Sum Divides the Product", Problem 10745, Amer. Math. Monthly, vol. 106 (1999), p. 587; vol. 108, (no. 7, Aug. 2001), pp. 668-669. [Gives upper bound]
|
|
EXAMPLE
|
There are 8 such solutions to rst = 5(r+s+t): (5, 4, 3), (7, 5, 2), (10, 4, 2), (11, 10, 1), (15, 8, 1), (20, 7, 1), (25, 3, 2), (35, 6, 1).
|
|
CROSSREFS
|
Cf. A018892, A004194, A063525.
More terms from David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001
Sequence in context: A106109 A123688 A082284 this_sequence A078677 A059770 A019690
Adjacent sequences: A063517 A063518 A063519 this_sequence A063521 A063522 A063523
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jud McCranie (j.mccranie(AT)comcast.net) and Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 01 2001
|
|
|
Search completed in 0.002 seconds
|
