A265738 Integers k such that k!3 is divisible by k^3, where k!3 = k!!! is a triple factorial number (A007661).

1, 18, 27, 36, 40, 45, 48, 54, 56, 60, 63, 64, 70, 72, 75, 77, 80, 81, 84, 88, 90, 91, 96, 98, 99, 100, 104, 105, 108, 110, 112, 117, 119, 120, 125, 126, 128, 130, 132, 133, 135, 136, 140, 143, 144, 147, 150, 152, 153, 154, 156, 160, 161, 162, 165, 168, 169, 170, 171, 175, 176

Offset

1,2

Comments

Obviously, a(n) cannot be a prime number. 77 is the first term which is semiprime.

Numbers of the form 9*t are terms of this sequence for t > 1.

Links

Table of n, a(n) for n=1..61.

Example

18 is a term because 18!!! = 524880 and 524880 mod 18^3 = 0.
27 is a term because 27!!! = 7142567040 and 7142567040 mod 27^3 = 0.

Prog

(PARI) tf(n) = prod(i=0, (n-1)\3, n-3*i);
k(n) = tf(n) % n^3;
for(n=1, 1e3, if(k(n)==0, print1(n, ", ")))

Crossrefs

Cf. A000578, A007661.

Sequence in context: A281918 A186129 A284672 * A151741 A090064 A082804

Adjacent sequences: A265735 A265736 A265737 * A265739 A265740 A265741

Keyword

nonn,easy

Author

Altug Alkan, Dec 15 2015

Status

approved