A051280 Numbers n such that n = k/d(k) has exactly 3 solutions, where d(k) = number of divisors of k.

3, 25, 40, 49, 54, 121, 125, 135, 140, 169, 189, 216, 220, 250, 260, 289, 297, 340, 351, 361, 375, 380, 400, 459, 460, 500, 513, 529, 580, 620, 621, 675, 729, 740, 770, 783, 820, 837, 841, 860, 875, 882, 910, 940, 961, 999, 1060, 1107, 1152, 1161, 1180, 1188, 1190

Offset

1,1

Comments

Many terms are of the form a(k) * p^m/(m+1), where p is coprime to the three solutions for k. The sequence of "primitive" terms (i.e. not expressible this way) begins 3, 40, 54, 125, 135, 216, 250.... Are there any such numbers that admit a fourth solution? - Charlie Neder, Feb 13 2019

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

There are exactly 3 numbers k, 9, 18 and 24, with k/d(k) = 3.

Mathematica

(Select[Table[k / Length @ Divisors[k], {k, 1, 200000}], IntegerQ] // Sort // Split // Select[#, Length[#] == 3 &] &)[[All, 1]][[1 ;; 53]] (* Jean-François Alcover, Apr 22 2011 *)

Crossrefs

Cf. A033950, A036763, A051278, A051279, A051346.

Sequence in context: A266702 A264937 A354725 * A145609 A259923 A120285

Adjacent sequences: A051277 A051278 A051279 * A051281 A051282 A051283

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, R. K. Guy, David W. Wilson

Status

approved