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A172292
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Triangle read by rows: T(n, k) = (2*n+1)*(2*k+1), n>=1, 1<=k<=n.
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2
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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
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OFFSET
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1,1
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COMMENTS
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A number m belongs to this sequence if and only if it is odd and composite.
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
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LINKS
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FORMULA
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T(n, k) = A144562(n,k)*2+3 read by rows. (Was old name.)
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EXAMPLE
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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.
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MATHEMATICA
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t[n_, k_]:= 4 n*k + 2n + 2k + 1; Table[t[n, k], {n, 15}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 20 2012 *)
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PROG
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(Magma) [4*n*k + 2*n + 2*k + 1: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 20 2012
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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