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

9, 15, 25, 21, 35, 49, 27, 45, 63, 81, 33, 55, 77, 99, 121, 39, 65, 91, 117, 143, 169, 45, 75, 105, 135, 165, 195, 225, 51, 85, 119, 153, 187, 221, 255, 289, 57, 95, 133, 171, 209, 247, 285, 323, 361, 63, 105, 147, 189, 231, 273, 315, 357, 399, 441, 69, 115, 161

Offset: 1

Author

Vincenzo Librandi, Nov 24 2010

Keywords

• nonn
• tabl
• easy

Comments

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

First column: A016945(n, n>=1), second column: A017329(n, n>=2), third column: A147587(n, n>=3). - Vincenzo Librandi, Nov 20 2012

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

Examples

			Triangle begins:
9;
15, 25;
21, 35,  49;
27, 45,  63,  81;
33, 55,  77,  99,  121;
39, 65,  91,  117, 143, 169;
45, 75,  105, 135, 165, 195, 225;
51, 85,  119, 153, 187, 221, 255, 289;
57, 95,  133, 171, 209, 247, 285, 323, 361;
63, 105, 147, 189, 231, 273, 315, 357, 399, 441; etc.
Number of occurrences:
  63 = 9*7 = 21*3 has two nontrivial factorizations, thus occurs twice.
		

Links

• Vincenzo Librandi, Rows n = 1..100, flattened
• OEIS Wiki, Odd composites

Crossrefs

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

Programs

Magma

[4*n*k + 2*n + 2*k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012

Mathematica

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

Formula

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

T(n, k) = 2*A083487(n, k)+1. - Daniel Forgues, Sep 20 2011