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 A265738 Integers k such that k!3 is divisible by k^3, where k!3 = k!!! is a triple factorial number (A007661). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified April 17 15:33 EDT 2021. Contains 343063 sequences. (Running on oeis4.)