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 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. 31
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Terms through row n, sorted, will provide terms for A077553 through row n*(n+1)/2. LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened 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 EXAMPLE Triangle begins: 4; 6, 9; 10, 15, 25; 14, 21, 35, 49; 22, 33, 55, 77, 121; 26, 39, 65, 91, 143, 169; 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 *) PROG (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 (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 CROSSREFS Cf. A100484 (left edge), A001248 (right edge), A143215 (row sums), A219603 (central terms of odd-indexed rows); A000040, A065342. Cf. A276086, A370121. Sequence in context: A178378 A133234 A111206 * A077554 A262812 A287296 Adjacent sequences: A087109 A087110 A087111 * A087113 A087114 A087115 KEYWORD nonn,tabl AUTHOR Ray Chandler, Aug 21 2003 STATUS approved

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Last modified September 12 09:16 EDT 2024. Contains 375850 sequences. (Running on oeis4.)