A173340 Numbers n for which the factorial of the number of divisors of n is divisible by n.

1, 2, 6, 8, 12, 18, 20, 24, 30, 36, 40, 42, 45, 48, 56, 60, 70, 72, 80, 84, 90, 96, 105, 108, 112, 120, 126, 128, 132, 140, 144, 150, 160, 162, 168, 180, 192, 198, 200, 210, 216, 220, 224, 240, 252, 264, 270, 280, 288, 300, 308, 312, 315, 320, 324, 330, 336, 350, 352, 360, 378, 384, 390, 396, 400, 405, 420, 432, 440

Offset: 1

Author

Robert Wintner, Nov 22 2010

Keywords

• nonn

Comments

An odd prime p can't be in this sequence because it only has two divisors and 2! does not divide p.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000142, A130674.

Programs

Magma

[ n: n in [1..1000] | Factorial(#Divisors(n)) mod n eq 0 ];

Mathematica

Select[Range[1000], Mod[DivisorSigma[0,#]!, #] == 0 &]