

A130799


Triangle read by rows in which row n (n>=3) list the antidivisors 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
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OFFSET

3,1


COMMENTS

A066272 gives the number of terms in each row.
See A066272 for definition of antidivisor.
2n1 and 2n+1 are twin primes (that is, n is in A040040) iff n has no odd antidivisors. For example, because n=15 has no odd antidivisors, 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 2n1 and 2n+1 (except 1, 2n+1 and 2n1). 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

Antidivisors 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



