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 A235671 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. Denominators are in A007395. Row sums give A074400. Row lengths is A114003 (see the Jovovic's formula in A114003). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE 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; ... MATHEMATICA pd[n_]:=Module[{d=Most[Divisors[n]]}, Flatten[Join[{d, {2n}, Reverse[d]}]]]; Flatten[Array[pd, 20]] (* Harvey P. Dale, Dec 22 2014 *) CROSSREFS Cf. A000005, A001065, A027750, A056538, A074400, A000203, A114002, A114003, A236104, A237591, A237593, A237270, A233772, A233773. Sequence in context: A131035 A339833 A118745 * A131034 A346873 A130313 Adjacent sequences:  A235668 A235669 A235670 * A235672 A235673 A235674 KEYWORD nonn,frac,tabf AUTHOR Omar E. Pol, Jan 24 2014 STATUS approved

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Last modified September 23 13:52 EDT 2021. Contains 347617 sequences. (Running on oeis4.)