A370135 Triangle read by rows: T(n,k) = (A002110(n) + A002110(k)) / A002110(k), 1 <= k <= n.

2, 4, 2, 16, 6, 2, 106, 36, 8, 2, 1156, 386, 78, 12, 2, 15016, 5006, 1002, 144, 14, 2, 255256, 85086, 17018, 2432, 222, 18, 2, 4849846, 1616616, 323324, 46190, 4200, 324, 20, 2, 111546436, 37182146, 7436430, 1062348, 96578, 7430, 438, 24, 2, 3234846616, 1078282206, 215656442, 30808064, 2800734, 215442, 12674, 668, 30, 2

Offset: 1

Author

Antti Karttunen, Mar 07 2024

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
          2;
          4,        2;
         16,        6,       2;
        106,       36,       8,       2;
       1156,      386,      78,      12,     2;
      15016,     5006,    1002,     144,    14,    2;
     255256,    85086,   17018,    2432,   222,   18,   2;
    4849846,  1616616,  323324,   46190,  4200,  324,  20,  2;
  111546436, 37182146, 7436430, 1062348, 96578, 7430, 438, 24, 2;
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..5050; the first 100 rows of triangle, flattened
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A002260, A370134, A370136 (arithmetic derivatives).

Programs

Mathematica

nn = 20; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn + 1]]]; Table[(P[n] + P[k])/P[k], {n, nn}, {k, n}] (* Michael De Vlieger, Mar 08 2024 *)

PARI

A002110(n) = prod(i=1,n,prime(i));
A370135(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2, x=A002110(1+n - binomial(c + 1, 2))); ((A002110(1+c)+x)/x); };

Formula

a(n) = A370134(n) / A002110(A002260(n)).