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

Author

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

Keywords

• nonn
• easy
• nice

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)