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A303557 a(0) = 1; a(n) = 2^(n-1)*prime(n)#, where prime(n)# is the product of first n primes.

%I A303557 #8 Apr 26 2018 17:43:59
%S A303557 1,2,12,120,1680,36960,960960,32672640,1241560320,57111774720,
%T A303557 3312482933760,205373941893120,15197671700090880,1246209079407452160,
%U A303557 107173980829040885760,10074354197929843261440,1067881544980563385712640,126010022307706479514091520,15373222721540190500719165440
%N A303557 a(0) = 1; a(n) = 2^(n-1)*prime(n)#, where prime(n)# is the product of first n primes.
%C A303557 For n > 0, a(n) is the smallest number m having exactly n distinct prime divisors and exactly 2*n - 1 prime divisors counted with multiplicity.
%H A303557 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%H A303557 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%F A303557 a(n) = A011782(n)*A002110(n).
%e A303557 a(1) = 2^1;
%e A303557 a(2) = 2^2*3;
%e A303557 a(3) = 2^3*3*5;
%e A303557 a(4) = 2^4*3*5*7;
%e A303557 a(5) = 2^5*3*5*7*11, etc.
%t A303557 Join[{1}, Table[2^(n - 1) Product[Prime[j], {j, n}], {n, 18}]]
%Y A303557 Central terms of triangle A303555 (for n > 0).
%Y A303557 Cf. A000079, A002110, A003680, A005179, A011782, A038547, A061283, A070175, A088860, A102476.
%K A303557 nonn
%O A303557 0,2
%A A303557 _Ilya Gutkovskiy_, Apr 26 2018