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A063525
Sum divides product: number of ordered triples of positive solutions (r,s,t) to the equation rst = n(r+s+t).
2
6, 15, 28, 30, 48, 45, 45, 78, 75, 54, 84, 94, 48, 105, 132, 105, 84, 99, 78, 189, 138, 60, 111, 210, 90, 132, 184, 129, 114, 153, 102, 228, 141, 105, 294, 267, 48, 132, 234, 228, 132, 159, 78, 300, 270, 96, 159, 301, 144, 231, 228, 162, 120, 297, 270, 429, 144, 72
OFFSET
1,1
LINKS
M. J. Pelling, Problem 10745, Amer. Math. Monthly, vol. 106 (1999), p. 587.
M. J. Pelling and F. W. Roush, The Sum Divides the Product: Problem 10745, Amer. Math. Monthly, vol. 108, (no. 7, Aug. 2001), pp. 668-669. [Gives upper bound]
EXAMPLE
The ordered solutions (r,s,t) of rst = 3(r+s+t) are (1,4,15), (1,5,9), (1,6,7), (2,2,12), (2,3,5), (3,3,3) for a total of 28 permuted solutions, hence a(3) = 28.
MATHEMATICA
np[{x_, y_, z_}] := If[x==y==z, 1, If[x==y || y==z, 3, 6]]; f[n_, t_] := Block[{s, r, sol = Reduce[r s t == n (r + s + t) && r >= s >= t , {r, s}, Integers]}, If[sol === False, 0, Total[np /@ ({r, s, t} /. List@ ToRules@ sol)]]]; a[n_] := Sum[f[n, t], {t, Sqrt[3 n]}]; Array[a, 58] (* Giovanni Resta, Jun 06 2019 *)
CROSSREFS
Cf. A063520.
Sequence in context: A353603 A165454 A333646 * A335267 A349476 A242454
KEYWORD
nonn
AUTHOR
Jud McCranie, Aug 01 2001
EXTENSIONS
More terms from David W. Wilson, Aug 01 2001
STATUS
approved