A303557 - OEIS

%I #8 Apr 26 2018 17:43:59

%S 1,2,12,120,1680,36960,960960,32672640,1241560320,57111774720,

%T 3312482933760,205373941893120,15197671700090880,1246209079407452160,

%U 107173980829040885760,10074354197929843261440,1067881544980563385712640,126010022307706479514091520,15373222721540190500719165440

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

%C 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 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%F a(n) = A011782(n)*A002110(n).

%e a(1) = 2^1;

%e a(2) = 2^2*3;

%e a(3) = 2^3*3*5;

%e a(4) = 2^4*3*5*7;

%e a(5) = 2^5*3*5*7*11, etc.

%t Join[{1}, Table[2^(n - 1) Product[Prime[j], {j, n}], {n, 18}]]

%Y Central terms of triangle A303555 (for n > 0).

%Y Cf. A000079, A002110, A003680, A005179, A011782, A038547, A061283, A070175, A088860, A102476.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 26 2018