A164853 - OEIS

%I #18 Feb 05 2020 16:54:38

%S 4,12,36,180,1260,1260,1260,13860,69300,900900,900900,15315300,

%T 15315300,290990700,290990700,6692786100,46849502700,46849502700,

%U 46849502700,46849502700,1358635578300,42117702927300,42117702927300,42117702927300

%N a(n) = lcm(first n semiprimes).

%C This is to A002110 Primorial numbers as semiprimes A001358 is to prime A000040.

%C a(n) = a(n-1) if A001358(n) is the product of two distinct odd primes. - _Robert Israel_, Feb 05 2020

%H Robert Israel, <a href="/A164853/b164853.txt">Table of n, a(n) for n = 1..1266</a>

%F a(n) = lcm_{i=1..n} A001358(i).

%F a(1) = A001358(1) = 4; a(n) = lcm(a(n-1), A001358(n)). - _Zak Seidov_, Aug 31 2009

%e a(1) = 4, the first semiprime. a(2) = lcm(4,6) = 12. a(3) = lcm(4,6,9) = 36.

%p N:= 10^3: # to use semiprimes <= N

%p SP:= select(t -> numtheory:-bigomega(t)=2, [$4..N]):

%p A[1]:= SP[1]:

%p for n from 2 to N do

%p A[n]:= ilcm(A[n-1],SP[n])

%p od:

%p seq(A[i],i=1..N); # _Robert Israel_, Feb 05 2020

%t With[{s=Select[Range[100],PrimeOmega[#]==2&]},Table[LCM@@Take[s,n],{n,Length[s]}]] (* _Harvey P. Dale_, May 05 2015 *)

%Y Cf. A001358, A002110.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 28 2009

%E More terms from _Zak Seidov_, Aug 31 2009