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A235671
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Triangle read by rows in which row n lists the proper divisors of n in increasing order, 2n, and the proper divisors of n in decreasing order.
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1
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2, 1, 4, 1, 1, 6, 1, 1, 2, 8, 2, 1, 1, 10, 1, 1, 2, 3, 12, 3, 2, 1, 1, 14, 1, 1, 2, 4, 16, 4, 2, 1, 1, 3, 18, 3, 1, 1, 2, 5, 20, 5, 2, 1, 1, 22, 1, 1, 2, 3, 4, 6, 24, 6, 4, 3, 2, 1, 1, 26, 1, 1, 2, 7, 28, 7, 2, 1, 1, 3, 5, 30, 5, 3, 1, 1, 2, 4, 8, 32, 8, 4, 2, 1
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OFFSET
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1,1
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COMMENTS
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Numerators of a sequence related to the symmetric structure of sigma, which arises from the structure of A237593. The structure in the first two octants is transformed in a structure in the 6th and 7th octants, which is similar to an isosceles triangle.
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LINKS
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EXAMPLE
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The irregular triangle begins:
2;
1, 4, 1;
1, 6, 1;
1, 2, 8, 2, 1;
1, 10, 1;
1, 2, 3, 12, 3, 2, 1;
1, 14, 1;
1, 2, 4, 16, 4, 2, 1;
1, 3, 18, 3, 1;
1, 2, 5, 20, 5, 2, 1;
1, 22, 1;
1, 2, 3, 4, 6, 24, 6, 4, 3, 2, 1;
...
Also:
1;
1/2, 2, 1/2;
1/2, 3, 1/2;
1/2, 1, 4, 1, 1/2;
1/2, 5, 1/2;
1/2, 1, 3/2, 6, 3/2, 1, 1/2;
1/2, 7, 1/2;
1/2, 1, 2, 8, 2, 1, 1/2;
1/2, 3/2, 9, 3/2, 1/2;
1/2, 1, 5/2, 10, 5/2, 1, 1/2;
1/2, 11, 1/2;
1/2, 1, 3/2, 2, 3, 12, 3, 2, 3/2, 1, 1/2;
...
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MATHEMATICA
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pd[n_]:=Module[{d=Most[Divisors[n]]}, Flatten[Join[{d, {2n}, Reverse[d]}]]]; Flatten[Array[pd, 20]] (* Harvey P. Dale, Dec 22 2014 *)
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CROSSREFS
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Cf. A000005, A001065, A027750, A056538, A074400, A000203, A114002, A114003, A236104, A237591, A237593, A237270, A233772, A233773.
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KEYWORD
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nonn,frac,tabf
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AUTHOR
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STATUS
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approved
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