A174903 Number of divisors d of n such that d

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 5, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 1, 6, 0, 0, 0, 3, 0, 3, 0, 0, 3, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 9, 0, 0, 1, 0, 0, 3, 0, 0, 0, 3, 0, 9, 0, 0, 2, 0, 1, 2, 0, 5, 0, 0, 0, 9, 0, 0, 0, 1, 0, 9, 1, 0, 0, 0, 0, 9, 0, 0, 1, 2, 0, 2, 0, 1, 4

Offset: 1

Author

Reinhard Zumkeller, Apr 01 2010

Keywords

• nonn

Examples

			a(12) = #{(2,3), (3,4), (4,6)} = 3;
a(15) = #{(3,5)} = 1;
a(18) = #{(2,3), (6,9)} = 2;
a(20) = #{(4,5)} = 1;
a(24) = #{(2,3), (3,4), (4,6), (6,8), (8,12)} = 5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A005279, A174904, A174905.

Programs

Haskell

import Data.List (intersect)
a174903 n = length [d | let ds = a027750_row n, d <- ds,
                    not $ null [e | e <- [d+1 .. 2*d-1] `intersect` ds]]
-- Reinhard Zumkeller, Sep 29 2014

Mathematica

a[n_] := Module[{d = Divisors[n]}, Count[d, ?(Length[Intersection[Range[# + 1, 2*# - 1], d]] > 0 &)]]; Array[a, 100] (* _Amiram Eldar, Apr 13 2024 *)

Formula

a(A174905(n)) = 0; a(A005279(n)) > 0.

a(A174904(n)) = n and a(m) <> n for m < A174904(n).

a(m)*a(n) <= a(m*n) for m, n coprime.