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

1, 2, 12, 120, 1680, 36960, 960960, 32672640, 1241560320, 57111774720, 3312482933760, 205373941893120, 15197671700090880, 1246209079407452160, 107173980829040885760, 10074354197929843261440, 1067881544980563385712640, 126010022307706479514091520, 15373222721540190500719165440

Offset: 0

Author

Ilya Gutkovskiy, Apr 26 2018

Keywords

• nonn

Comments

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.

Examples

			a(1) = 2^1;
a(2) = 2^2*3;
a(3) = 2^3*3*5;
a(4) = 2^4*3*5*7;
a(5) = 2^5*3*5*7*11, etc.
		

Links

• Index entries for sequences related to primorial numbers
• Index to sequences related to prime signature

Crossrefs

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

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

Programs

Mathematica

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

Formula

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