A241556 Number of prime anti-divisors m of n.

0, 0, 1, 1, 2, 0, 3, 2, 1, 2, 3, 1, 3, 1, 1, 2, 5, 2, 3, 2, 1, 2, 3, 1, 4, 2, 3, 4, 3, 0, 3, 4, 3, 2, 3, 0, 3, 4, 3, 1, 2, 2, 5, 2, 3, 4, 5, 2, 3, 2, 1, 3, 4, 0, 3, 2, 3, 4, 5, 3, 4, 3, 2, 2, 3, 2, 5, 2, 1, 2, 5, 4, 5, 2, 1, 2, 5, 2, 3, 4, 3, 3, 4, 1, 4, 2, 3, 4, 3, 0, 3, 4, 5, 4, 3, 0

Offset: 1

Author

Michael De Vlieger, Aug 08 2014

Keywords

• nonn

Comments

The maximum value of a(n) is 9 for 1 <= n <= 10000.

There are 167 instances of a(n) = 0 for 1 <= n <= 10000 (See A241557).

Examples

			a(10) = 2, since 10 has 3 anti-divisors {3, 4, 7}; only {3, 7} are prime.
a(9223) = 9; these are {2, 3, 5, 7, 11, 13, 17, 31, 43}.
		

Links

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

Crossrefs

Cf. A066272, A192281, A242965, A242966, A241557.

Programs

Mathematica

primeAntiDivisors[n_] := Select[Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)], PrimeQ]; a241556[n_Integer] := Map[Length[primeAntiDivisors[#]] &, Range[n]]; a241556[120]