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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.

%I A350455 #25 Jan 04 2022 18:29:11
%S A350455 4,9,15,21,25,35,33,49,39,55,65,77,51,91,57,85,121,95,119,143,69,133,
%T A350455 169,115,187,161,209,221,87,247,93,145,253,289,155,203,299,323,217,
%U A350455 361,111,319,391,185,341,377,437,123,259,403,129,205,493,529,215,287,407
%N 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.
%C A350455 Assuming Goldbach's conjecture, no row is empty.
%H A350455 Alois P. Heinz, <a href="/A350455/b350455.txt">Rows n = 2..1000, flattened</a>
%H A350455 Wikipedia, <a href="https://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>
%e A350455 Triangle T(n,k) begins:
%e A350455     4;
%e A350455     9;
%e A350455    15;
%e A350455    21,  25;
%e A350455    35     ;
%e A350455    33,  49;
%e A350455    39,  55;
%e A350455    65,  77;
%e A350455    51,  91;
%e A350455    57,  85, 121;
%e A350455    95, 119, 143;
%e A350455    69, 133, 169;
%e A350455   115, 187     ;
%e A350455   161, 209, 221;
%e A350455    87, 247     ;
%e A350455    93, 145, 253, 289;
%e A350455   155, 203, 299, 323;
%e A350455   ...
%p A350455 T:= n-> seq(`if`(andmap(isprime, [h, 2*n-h]), h*(2*n-h), [][]), h=2..n):
%p A350455 seq(T(n), n=2..30);
%Y A350455 Column k=1 gives A073046.
%Y A350455 Last elements of rows give A102084.
%Y A350455 Row sums give A228553.
%Y A350455 Row products give A337568.
%Y A350455 Row lengths give A045917.
%Y A350455 Cf. A000040, A001358, A046315, A350419.
%K A350455 nonn,look,tabf
%O A350455 2,1
%A A350455 _Alois P. Heinz_, Dec 31 2021