A273323 a(n) = greatest number k <= n^2 having exactly n divisors, or 0 if no such k exists.

1, 3, 9, 15, 16, 32, 0, 56, 36, 80, 0, 140, 0, 192, 144, 216, 0, 300, 0, 336, 0, 0, 0, 540, 0, 0, 0, 0, 0, 720, 0, 840, 0, 0, 0, 1260, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Carlos Eduardo Olivieri, May 20 2016

Keywords

• nonn
• easy

Comments

The sequence is zero for n>36, since A005179(n) > n^2 for all n > 36.

Examples

			a(4) = 15, because 15 is the greatest number <= 4^2 with exactly 4 divisors.
		

Crossrefs

Cf. A000005, A005179, A035033.

Programs

Mathematica

Seq := {}; For[n = 1, n < 50, n++, AppendTo[Seq, a = Max[Select[Range[n^2], DivisorSigma[0, #] == n &]]; If[a == -Infinity, 0, a]]]; Seq