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

Author

Michael De Vlieger, Aug 11 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• M. De Vlieger, Arithmetic Relationships between Antidivisors k < n and n

Crossrefs

Cf. A066272, A240979.

Programs

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 *)