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

%I A306237 #38 Jan 10 2021 13:30:55
%S A306237 3,10,42,330,2730,39270,570570,11741730,281291010,6915878970,
%T A306237 239378649510,8222980095330,319091739796830,14299762385778870,
%U A306237 693386350578511590,36278497172720993190,1987938667108592728530,128824943460332246817690,8327475076517894939812170,573657473228859495079173570
%N A306237 a(n) = primorial prime(n)#/prime(n - 1).
%C A306237 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).
%H A306237 Michael De Vlieger, <a href="/A306237/b306237.txt">Table of n, a(n) for n = 2..351</a>
%H A306237 Michael De Vlieger, <a href="/A306237/a306237.png">Chart plotting terms m in A306237 at (x, y) where x = A000720(A006530(m)) and y = A000010(m)/m</a>
%H A306237 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A306237 a(n) = A002110(n)/A000040(n - 1).
%e A306237 a(2) = (2 * 3)/prime(2 - 1) = 6/2 = 3.
%e A306237 a(3) = (2*3*5)/prime(3 - 1) = 30/3 = 10.
%p A306237 a:= proc(n) option remember; `if`(n=2, 3,
%p A306237       a(n-1)*(p-> p(n-2)/p(n-1)*p(n))(ithprime))
%p A306237     end:
%p A306237 seq(a(n), n=2..23);  # _Alois P. Heinz_, Jan 10 2021
%t A306237 Array[Product[Prime@ i, {i, #}]/Prime[# - 1] &, 20, 2]
%o A306237 (PARI) a(n) = prod(k=1, n, prime(k))/prime(n-1); \\ _Michel Marcus_, Apr 13 2019
%Y A306237 Cf. A000040, A002110.
%K A306237 nonn,easy
%O A306237 2,1
%A A306237 _Michael De Vlieger_, Apr 10 2019