A218558 - OEIS

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A218558

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

8, 12, 27, 42, 42, 52, 63, 75, 92, 92, 102, 114, 124, 138, 147, 153, 164, 171, 182, 195, 207, 212, 222, 231, 242, 255, 261, 273, 282, 292, 310, 316, 322, 332, 343, 354, 363, 374, 385, 399, 402, 412, 423, 434, 442, 452, 465, 474, 483, 494, 506

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OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..51.

FORMULA

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

EXAMPLE

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

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

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

PROG

(PARI) a(n)=n*=10; while(bigomega(n++)!=3, ); n \\ Charles R Greathouse IV, Aug 30 2017

CROSSREFS

Cf. A008592, A014612, A218255, A185008.