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A172292 Triangle read by rows: T(n, k) = (2*n+1)*(2*k+1), n>=1, 1<=k<=n. 2

%I

%S 9,15,25,21,35,49,27,45,63,81,33,55,77,99,121,39,65,91,117,143,169,45,

%T 75,105,135,165,195,225,51,85,119,153,187,221,255,289,57,95,133,171,

%U 209,247,285,323,361,63,105,147,189,231,273,315,357,399,441,69,115,161

%N Triangle read by rows: T(n, k) = (2*n+1)*(2*k+1), n>=1, 1<=k<=n.

%C A number m belongs to this sequence if and only if it is odd and composite.

%C First column: A016945(n, n>=1), second column: A017329(n, n>=2), third column: A147587(n, n>=3). - _Vincenzo Librandi_, Nov 20 2012

%C The number of occurrences of m corresponds to the number of nontrivial factorizations of m, i.e., A072670(m-1). - _Daniel Forgues_, Apr 22 2014

%H Vincenzo Librandi, <a href="/A172292/b172292.txt">Rows n = 1..100, flattened</a>

%H OEIS Wiki, <a href="/wiki/Odd_composites">Odd composites</a>

%F T(n, k) = A144562(n,k)*2+3 read by rows. (Was old name.)

%F T(n, k) = 2*A083487(n, k)+1. - _Daniel Forgues_, Sep 20 2011

%e Triangle begins:

%e 9;

%e 15, 25;

%e 21, 35, 49;

%e 27, 45, 63, 81;

%e 33, 55, 77, 99, 121;

%e 39, 65, 91, 117, 143, 169;

%e 45, 75, 105, 135, 165, 195, 225;

%e 51, 85, 119, 153, 187, 221, 255, 289;

%e 57, 95, 133, 171, 209, 247, 285, 323, 361;

%e 63, 105, 147, 189, 231, 273, 315, 357, 399, 441; etc.

%e Number of occurrences:

%e 63 = 9*7 = 21*3 has two nontrivial factorizations, thus occurs twice.

%t t[n_,k_]:= 4 n*k + 2n + 2k + 1; Table[t[n, k], {n,15}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 20 2012 *)

%o (MAGMA) [4*n*k + 2*n + 2*k + 1: k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 20 2012

%Y Cf. A144562, A083487, A016945, A017329, A147587.

%K nonn,tabl,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 24 2010

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Last modified July 30 15:06 EDT 2021. Contains 346359 sequences. (Running on oeis4.)