A350455 T(n,k) is the k-th semiprime whose sum of prime factors equals 2n, triangle T(n,k), n>=2, 1<=k<=A045917(n), read by rows.

4, 9, 15, 21, 25, 35, 33, 49, 39, 55, 65, 77, 51, 91, 57, 85, 121, 95, 119, 143, 69, 133, 169, 115, 187, 161, 209, 221, 87, 247, 93, 145, 253, 289, 155, 203, 299, 323, 217, 361, 111, 319, 391, 185, 341, 377, 437, 123, 259, 403, 129, 205, 493, 529, 215, 287, 407

Offset: 2

Author

Alois P. Heinz, Dec 31 2021

Keywords

• nonn
• look
• tabf

Comments

Assuming Goldbach's conjecture, no row is empty.

Examples

			Triangle T(n,k) begins:
    4;
    9;
   15;
   21,  25;
   35     ;
   33,  49;
   39,  55;
   65,  77;
   51,  91;
   57,  85, 121;
   95, 119, 143;
   69, 133, 169;
  115, 187     ;
  161, 209, 221;
   87, 247     ;
   93, 145, 253, 289;
  155, 203, 299, 323;
  ...
		

Links

• Alois P. Heinz, Rows n = 2..1000, flattened
• Wikipedia, Goldbach's conjecture

Crossrefs

Column k=1 gives A073046.

Last elements of rows give A102084.

Row sums give A228553.

Row products give A337568.

Row lengths give A045917.

Cf. A000040, A001358, A046315, A350419.

Programs

Maple

T:= n-> seq(`if`(andmap(isprime, [h, 2*n-h]), h*(2*n-h), [][]), h=2..n):
seq(T(n), n=2..30);