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A173340
Numbers n for which the factorial of the number of divisors of n is divisible by n.
1
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
MATHEMATICA
Select[Range[1000], Mod[DivisorSigma[0, #]!, #] == 0 &]
PROG
(Magma) [ n: n in [1..1000] | Factorial(#Divisors(n)) mod n eq 0 ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Wintner, Nov 22 2010
STATUS
approved