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A242029
Number of anti-divisors m <= n of n that are coprime to n.
2
0, 0, 1, 1, 2, 0, 3, 2, 1, 2, 3, 1, 4, 2, 1, 2, 5, 2, 3, 2, 1, 4, 5, 1, 4, 2, 3, 4, 3, 0, 5, 6, 3, 2, 3, 0, 5, 6, 3, 3, 4, 2, 5, 2, 3, 4, 5, 2, 5, 4, 1, 6, 7, 0, 3, 2, 3, 6, 7, 3, 4, 4, 3, 2, 3, 2, 9, 6, 1, 2, 5, 4, 7, 4, 1, 4, 7, 2, 3, 4, 3, 6, 7, 1, 6, 4, 5
OFFSET
1,5
COMMENTS
See A066272 for the definition of anti-divisor; that sequence gives the number of anti-divisors m < n of n.
All the anti-divisors m < n of prime n must be coprime to n, since any integer k > 1 must either divide or be coprime to prime n, and since no anti-divisor m can divide n.
EXAMPLE
a(3) = 1 and A066272(3) = 1 because the set of anti-divisors of 3 = {2} and 2 is coprime to 3.
a(6) = 0 and A066272(6) = 1 because the set of anti-divisors of 6 = {4} but 4 is not coprime to 6.
a(12) = 1 and A066272(12) = 2 because the set of anti-divisors of 12 = {5, 8}, but only 5 is coprime to 12.
MATHEMATICA
antiDivisors[n_Integer] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; a242029[n_Integer] := Length[Select[antiDivisors[n], CoprimeQ[#, n] &]]; Table[a242029[k], {k, 100}] (* Michael De Vlieger, Aug 11 2014 *)
CROSSREFS
Sequence in context: A325195 A026728 A241556 * A090722 A221879 A171934
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Aug 11 2014
STATUS
approved