A242029 Number of anti-divisors m <= n of n that are coprime to n.

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.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

M. De Vlieger, Arithmetic Relationships between Antidivisors k < n and 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

Cf. A066272, A240979.

Sequence in context: A325195 A026728 A241556 * A090722 A221879 A171934

Adjacent sequences: A242026 A242027 A242028 * A242030 A242031 A242032

Keyword

nonn

Author

Michael De Vlieger, Aug 11 2014

Status

approved