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

1,2

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A000142, A130674.

Sequence in context: A008407 A111224 A139718 * A135311 A200568 A162860

Adjacent sequences: A173337 A173338 A173339 * A173341 A173342 A173343

Keyword

nonn

Author

Robert Wintner, Nov 22 2010

Status

approved