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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 08:20 EDT 2021. Contains 346422 sequences. (Running on oeis4.)