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 A130799 Triangle read by rows in which row n (n>=3) list the anti-divisors of n. 13
 2, 3, 2, 3, 4, 2, 3, 5, 3, 5, 2, 6, 3, 4, 7, 2, 3, 7, 5, 8, 2, 3, 5, 9, 3, 4, 9, 2, 6, 10, 3, 11, 2, 3, 5, 7, 11, 4, 5, 7, 12, 2, 3, 13, 3, 8, 13, 2, 6, 14, 3, 4, 5, 9, 15, 2, 3, 5, 9, 15, 7, 16, 2, 3, 7, 10, 17, 3, 4, 17, 2, 5, 6, 11, 18, 3, 5, 8, 11, 19, 2, 3, 19, 4, 12, 20, 2, 3, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS A066272 gives the number of terms in each row. See A066272 for definition of anti-divisor. 2n-1 and 2n+1 are twin primes (that is, n is in A040040) iff n has no odd anti-divisors. For example, because n=15 has no odd anti-divisors, 29 and 31 are twin primes. - Jon Perry, Sep 12 2012 Row n is all the numbers which are: (a) 2n divided by its odd divisors (except 1), and (b) the divisors of 2n-1 and 2n+1 (except 1, 2n+1 and 2n-1). For example, n=18: odd divisors of 36 are {3,9} and 36/{3,9} = {4,12}; divisors of 35 are {5,7} and divisors of 37 are null (37 is prime).  Therefore row 18 is 4,5,7 and 12.  See A066542 for further explanation. - Bob Selcoe, Feb 24 2014 LINKS T. D. Noe, Rows n=3..1000 of triangle, flattened Diana Mecum, Rows 3 through 500 EXAMPLE Anti-divisors of 3 through 20: 3: 2 4: 3 5: 2, 3 6: 4 7: 2, 3, 5 8: 3, 5 9: 2, 6 10: 3, 4, 7 11: 2, 3, 7 12: 5, 8 13: 2, 3, 5, 9 14: 3, 4, 9 15: 2, 6, 10 16: 3, 11 17: 2, 3, 5, 7, 11 18: 4, 5, 7, 12 19: 2, 3, 13 20: 3, 8, 13 MATHEMATICA f[n_] := Complement[ Sort@ Join[ Select[ Union@ Flatten@ Divisors[{2 n - 1, 2 n + 1}], OddQ@ # && # < n &], Select[ Divisors[2 n], EvenQ@ # && # < n &]], Divisors@ n]; Flatten@ Table[ f@n, {n, 3, 32}] (* Robert G. Wilson v, Jul 17 2007 *) Table[Select[Range[2, n - 1], Abs[Mod[n, #] - #/2] < 1 &], {n, 3, 31}] // Flatten (* Michael De Vlieger, Jun 14 2016, after Harvey P. Dale at A066272 *) CROSSREFS Sequence in context: A237582 A097352 A076050 * A243519 A278102 A106383 Adjacent sequences:  A130796 A130797 A130798 * A130800 A130801 A130802 KEYWORD nonn,tabf AUTHOR Diana L. Mecum, Jul 17 2007 STATUS approved

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Last modified January 19 21:52 EST 2019. Contains 319310 sequences. (Running on oeis4.)