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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.

%I A087112 #31 Jun 25 2024 08:18:07
%S A087112 4,6,9,10,15,25,14,21,35,49,22,33,55,77,121,26,39,65,91,143,169,34,51,
%T A087112 85,119,187,221,289,38,57,95,133,209,247,323,361,46,69,115,161,253,
%U A087112 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 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.
%C A087112 Terms through row n, sorted, will provide terms for A077553 through row n*(n+1)/2.
%H A087112 Reinhard Zumkeller, <a href="/A087112/b087112.txt">Rows n = 1..125 of triangle, flattened</a>
%F A087112 The n-th row consists of n terms, prime(n)*prime(i), i=1..n.
%F A087112 T(n, k) = A000040(n) * A000040(k).
%F A087112 For n >= 2, a(n) = A276086(A370121(n-1)). - _Antti Karttunen_, Feb 29 2024
%e A087112 Triangle begins:
%e A087112    4;
%e A087112    6,   9;
%e A087112   10,  15,  25;
%e A087112   14,  21,  35,  49;
%e A087112   22,  33,  55,  77, 121;
%e A087112   26,  39,  65,  91, 143, 169;
%p A087112 T := (n, k) -> ithprime(n) * ithprime(k):
%p A087112 seq(print(seq(T(n, k), k = 1..n)), n = 1..11);  # _Peter Luschny_, Jun 25 2024
%t A087112 Table[ Prime[j]*Prime[k], {j, 11}, {k, j}] // Flatten (* _Robert G. Wilson v_, Feb 06 2017 *)
%o A087112 (Haskell)
%o A087112 a087112 n k = a087112_tabl !! (n-1) !! (k-1)
%o A087112 a087112_row n = map (* last ps) ps where ps = take n a000040_list
%o A087112 a087112_tabl = map a087112_row [1..]
%o A087112 -- _Reinhard Zumkeller_, Nov 25 2012
%o A087112 (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 A087112 Cf. A100484 (left edge), A001248 (right edge), A143215 (row sums), A219603 (central terms of odd-indexed rows); A000040, A065342.
%Y A087112 Cf. A276086, A370121.
%K A087112 nonn,tabl
%O A087112 1,1
%A A087112 _Ray Chandler_, Aug 21 2003