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Next number that is the product of exactly three (not necessarily distinct) primes, after 10*n.
0

%I #12 Aug 30 2017 03:01:37

%S 8,12,27,42,42,52,63,75,92,92,102,114,124,138,147,153,164,171,182,195,

%T 207,212,222,231,242,255,261,273,282,292,310,316,322,332,343,354,363,

%U 374,385,399,402,412,423,434,442,452,465,474,483,494,506

%N Next number that is the product of exactly three (not necessarily distinct) primes, after 10*n.

%C This is to "triprimes" A014612 as A185008 is to semiprimes A001358, and as A218255 is to primes A000040.

%C The first equal terms are a(4) = a(5) = 42. The density of numbers n such that a(n) = a(n+1) is 1. Similarly, the density of numbers n such that a(n) = a(n+1) = ... = a(n+k) is 1 for any fixed k. - _Charles R Greathouse IV_, Aug 30 2017

%F a(n) = MIN[k in A014612 and k > 10*n = A008592(n)].

%e a(0) = 8, the first number that is the product of exactly three (not necessarily distinct) primes.

%e a(1) = 12 = 2^2 * 3, which is >10*1=10.

%e a(3) = 42 even though 30 = 2*3*5 is a "triprime" because we use ">" rather that ">=" in the definition.

%o (PARI) a(n)=n*=10; while(bigomega(n++)!=3, ); n \\ _Charles R Greathouse IV_, Aug 30 2017

%Y Cf. A008592, A014612, A218255, A185008.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Nov 02 2012

%E Offset corrected by _Charles R Greathouse IV_, Aug 30 2017