A173340 - OEIS

%I #22 Sep 08 2022 08:45:50

%S 1,2,6,8,12,18,20,24,30,36,40,42,45,48,56,60,70,72,80,84,90,96,105,

%T 108,112,120,126,128,132,140,144,150,160,162,168,180,192,198,200,210,

%U 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

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

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

%H Amiram Eldar, <a href="/A173340/b173340.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%Y Cf. A000005, A000142, A130674.

%K nonn

%O 1,2

%A _Robert Wintner_, Nov 22 2010