A087112 Triangle in which the n-th row contains n distinct semiprimes not listed previously with all prime factors from among the first n primes.

4, 6, 9, 10, 15, 25, 14, 21, 35, 49, 22, 33, 55, 77, 121, 26, 39, 65, 91, 143, 169, 34, 51, 85, 119, 187, 221, 289, 38, 57, 95, 133, 209, 247, 323, 361, 46, 69, 115, 161, 253, 299, 391, 437, 529, 58, 87, 145, 203, 319, 377, 493, 551, 667, 841, 62, 93, 155, 217, 341, 403, 527, 589, 713, 899, 961

Offset: 1

Author

Ray Chandler, Aug 21 2003

Keywords

• nonn
• tabl

Comments

Terms through row n, sorted, will provide terms for A077553 through row n*(n+1)/2.

Examples

			Triangle begins:
   4;
   6,   9;
  10,  15,  25;
  14,  21,  35,  49;
  22,  33,  55,  77, 121;
  26,  39,  65,  91, 143, 169;
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A100484 (left edge), A001248 (right edge), A143215 (row sums), A219603 (central terms of odd-indexed rows); A000040, A065342.

Cf. A276086, A370121.

Programs

Haskell

a087112 n k = a087112_tabl !! (n-1) !! (k-1)
a087112_row n = map (* last ps) ps where ps = take n a000040_list
a087112_tabl = map a087112_row [1..]
-- Reinhard Zumkeller, Nov 25 2012

Maple

T := (n, k) -> ithprime(n) * ithprime(k):
seq(print(seq(T(n, k), k = 1..n)), n = 1..11);  # Peter Luschny, Jun 25 2024

Mathematica

Table[ Prime[j]*Prime[k], {j, 11}, {k, j}] // Flatten (* Robert G. Wilson v, Feb 06 2017 *)

PARI

A087112(n) = { n--; my(c = (sqrtint(8*n + 1) - 1) \ 2); (prime(1+c) * prime(1+(n-binomial(1+c, 2)))); }; \\ Antti Karttunen, Feb 29 2024

Formula

The n-th row consists of n terms, prime(n)*prime(i), i=1..n.

T(n, k) = A000040(n) * A000040(k).

For n >= 2, a(n) = A276086(A370121(n-1)). - Antti Karttunen, Feb 29 2024