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

%I A172292 #43 Sep 08 2022 08:45:50
%S A172292 9,15,25,21,35,49,27,45,63,81,33,55,77,99,121,39,65,91,117,143,169,45,
%T A172292 75,105,135,165,195,225,51,85,119,153,187,221,255,289,57,95,133,171,
%U A172292 209,247,285,323,361,63,105,147,189,231,273,315,357,399,441,69,115,161
%N A172292 Triangle read by rows: T(n, k) = (2*n+1)*(2*k+1), n>=1, 1<=k<=n.
%C A172292 A number m belongs to this sequence if and only if it is odd and composite.
%C A172292 First column: A016945(n, n>=1), second column: A017329(n, n>=2), third column: A147587(n, n>=3). - _Vincenzo Librandi_, Nov 20 2012
%C A172292 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 A172292 Vincenzo Librandi, <a href="/A172292/b172292.txt">Rows n = 1..100, flattened</a>
%H A172292 OEIS Wiki, <a href="/wiki/Odd_composites">Odd composites</a>
%F A172292 T(n, k) = A144562(n,k)*2+3 read by rows. (Was old name.)
%F A172292 T(n, k) = 2*A083487(n, k)+1. - _Daniel Forgues_, Sep 20 2011
%e A172292 Triangle begins:
%e A172292 9;
%e A172292 15, 25;
%e A172292 21, 35,  49;
%e A172292 27, 45,  63,  81;
%e A172292 33, 55,  77,  99,  121;
%e A172292 39, 65,  91,  117, 143, 169;
%e A172292 45, 75,  105, 135, 165, 195, 225;
%e A172292 51, 85,  119, 153, 187, 221, 255, 289;
%e A172292 57, 95,  133, 171, 209, 247, 285, 323, 361;
%e A172292 63, 105, 147, 189, 231, 273, 315, 357, 399, 441; etc.
%e A172292 Number of occurrences:
%e A172292   63 = 9*7 = 21*3 has two nontrivial factorizations, thus occurs twice.
%t A172292 t[n_,k_]:= 4 n*k + 2n + 2k + 1; Table[t[n, k], {n,15}, {k, n}]//Flatten (* _Vincenzo Librandi_, Nov 20 2012 *)
%o A172292 (Magma) [4*n*k + 2*n + 2*k + 1: k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Nov 20 2012
%Y A172292 Cf. A144562, A083487, A016945, A017329, A147587.
%K A172292 nonn,tabl,easy
%O A172292 1,1
%A A172292 _Vincenzo Librandi_, Nov 24 2010