A374000 - OEIS

%I #4 Jul 07 2024 20:58:35

%S 15,385,1001,5005,85085,323323,7436429,955049953,

%T 183698727318433150098859517,35336848261,435656388001,

%U 3868985835982814590518552822749329543261,1448810778701,20475850236047,5663533044013,343523383391078124677551786579090220816600929,62298863484143

%N a(n) = Product_{i=1..m} prime(k + T(n,i)) where k = pi(A186702(n)), T(n,i) is the i-th term in row n of A186634, and m = length of row n of A186634.

%e Let p = A186702 and let T(n,i) be the i-th term in row n of A186634.

%e a(1) = 15 since p(1) = 3 and row 1 of T is {0, 2}, hence 3 * (3+2) = 3 * 5 = 15.

%e a(2) = 385 since p(2) = 5 and row 2 of T is {0, 2, 4}, hence 5 * (5+2) * (5+2+4) = 5*7*11 = 385.

%e Prime decomposition of the first 8 terms.

%e         a(n)    k  k+m-1  prime decomposition.

%e ----------------------------------------------

%e          15     2     3    3 *  5

%e         385     3     5    5 *  7 * 11

%e        1001     4     6    7 * 11 * 13

%e        5005     3     6    5 *  7 * 11 * 13

%e       85085     3     7    5 *  7 * 11 * 13 * 17

%e      323323     4     8    7 * 11 * 13 * 17 * 19

%e     7436429     4     9    7 * 11 * 13 * 17 * 19 * 23

%e   955049953     5    11   11 * 13 * 17 * 19 * 23 * 29 * 31

%Y Cf. A005117, A120944, A186634, A186702.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Jul 04 2024