A306237 a(n) = primorial prime(n)#/prime(n - 1).

3, 10, 42, 330, 2730, 39270, 570570, 11741730, 281291010, 6915878970, 239378649510, 8222980095330, 319091739796830, 14299762385778870, 693386350578511590, 36278497172720993190, 1987938667108592728530, 128824943460332246817690, 8327475076517894939812170, 573657473228859495079173570

Offset: 2

Author

Michael De Vlieger, Apr 10 2019

Keywords

• nonn
• easy

Comments

Let primorial p_n# = A002110(n) and prime(n - 1) = A000040(n - 1). This sequence can be defined alternatively as p_(n - 2) * prime(n).

Examples

			a(2) = (2 * 3)/prime(2 - 1) = 6/2 = 3.
a(3) = (2*3*5)/prime(3 - 1) = 30/3 = 10.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..351
• Michael De Vlieger, Chart plotting terms m in A306237 at (x, y) where x = A000720(A006530(m)) and y = A000010(m)/m
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A000040, A002110.

Programs

Maple

a:= proc(n) option remember; `if`(n=2, 3,
      a(n-1)*(p-> p(n-2)/p(n-1)*p(n))(ithprime))
    end:
seq(a(n), n=2..23);  # Alois P. Heinz, Jan 10 2021

Mathematica

Array[Product[Prime@ i, {i, #}]/Prime[# - 1] &, 20, 2]

PARI

a(n) = prod(k=1, n, prime(k))/prime(n-1); \\ Michel Marcus, Apr 13 2019

Formula

a(n) = A002110(n)/A000040(n - 1).