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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.
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%I #25 Jan 04 2022 18:29:11

%S 4,9,15,21,25,35,33,49,39,55,65,77,51,91,57,85,121,95,119,143,69,133,

%T 169,115,187,161,209,221,87,247,93,145,253,289,155,203,299,323,217,

%U 361,111,319,391,185,341,377,437,123,259,403,129,205,493,529,215,287,407

%N 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 Assuming Goldbach's conjecture, no row is empty.

%H Alois P. Heinz, <a href="/A350455/b350455.txt">Rows n = 2..1000, flattened</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Goldbach%27s_conjecture">Goldbach's conjecture</a>

%e Triangle T(n,k) begins:

%e 4;

%e 9;

%e 15;

%e 21, 25;

%e 35 ;

%e 33, 49;

%e 39, 55;

%e 65, 77;

%e 51, 91;

%e 57, 85, 121;

%e 95, 119, 143;

%e 69, 133, 169;

%e 115, 187 ;

%e 161, 209, 221;

%e 87, 247 ;

%e 93, 145, 253, 289;

%e 155, 203, 299, 323;

%e ...

%p T:= n-> seq(`if`(andmap(isprime, [h, 2*n-h]), h*(2*n-h), [][]), h=2..n):

%p seq(T(n), n=2..30);

%Y Column k=1 gives A073046.

%Y Last elements of rows give A102084.

%Y Row sums give A228553.

%Y Row products give A337568.

%Y Row lengths give A045917.

%Y Cf. A000040, A001358, A046315, A350419.

%K nonn,look,tabf

%O 2,1

%A _Alois P. Heinz_, Dec 31 2021