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%I #10 Dec 20 2015 14:04:58
%S 1,18,27,36,40,45,48,54,56,60,63,64,70,72,75,77,80,81,84,88,90,91,96,
%T 98,99,100,104,105,108,110,112,117,119,120,125,126,128,130,132,133,
%U 135,136,140,143,144,147,150,152,153,154,156,160,161,162,165,168,169,170,171,175,176
%N Integers k such that k!3 is divisible by k^3, where k!3 = k!!! is a triple factorial number (A007661).
%C Obviously, a(n) cannot be a prime number. 77 is the first term which is semiprime.
%C Numbers of the form 9*t are terms of this sequence for t > 1.
%e 18 is a term because 18!!! = 524880 and 524880 mod 18^3 = 0.
%e 27 is a term because 27!!! = 7142567040 and 7142567040 mod 27^3 = 0.
%o (PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
%o k(n) = tf(n) % n^3;
%o for(n=1, 1e3, if(k(n)==0, print1(n, ", ")))
%Y Cf. A000578, A007661.
%K nonn,easy
%O 1,2
%A _Altug Alkan_, Dec 15 2015