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%I #29 Mar 09 2024 08:18:57
%S 4,6,9,10,15,25,14,21,35,49,22,33,55,77,121,26,39,65,91,143,169,34,51,
%T 85,119,187,221,289,38,57,95,133,209,247,323,361,46,69,115,161,253,
%U 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
%N Triangle in which the n-th row contains n distinct semiprimes not listed previously with all prime factors from among the first n primes.
%C Terms through row n, sorted, will provide terms for A077553 through row n*(n+1)/2.
%H Reinhard Zumkeller, <a href="/A087112/b087112.txt">Rows n = 1..125 of triangle, flattened</a>
%F The n-th row consists of n terms, prime(n)*prime(i), i=1..n.
%F T(n,k) = A000040(n) * A000040(k).
%F For n >= 2, a(n) = A276086(A370121(n-1)). - _Antti Karttunen_, Feb 29 2024
%e Triangle begins:
%e 4;
%e 6, 9;
%e 10, 15, 25;
%e 14, 21, 35, 49;
%e 22, 33, 55, 77, 121;
%e 26, 39, 65, 91, 143, 169;
%t Table[ Prime[j]*Prime[k], {j, 11}, {k, j}] // Flatten (* _Robert G. Wilson v_, Feb 06 2017 *)
%o (Haskell)
%o a087112 n k = a087112_tabl !! (n-1) !! (k-1)
%o a087112_row n = map (* last ps) ps where ps = take n a000040_list
%o a087112_tabl = map a087112_row [1..]
%o -- _Reinhard Zumkeller_, Nov 25 2012
%o (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
%Y Cf. A100484 (left edge), A001248 (right edge), A143215 (row sums), A219603 (central terms of odd-indexed rows); A000040, A065342.
%Y Cf. A276086, A370121.
%K nonn,tabl
%O 1,1
%A _Ray Chandler_, Aug 21 2003
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