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A130799
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Triangle read by rows in which row n (n>=3) list the anti-divisors of n.
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15
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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
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3,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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