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A174903 Number of divisors d of n such that d for at least another divisor e of n.

%I A174903 #11 Apr 13 2024 05:12:53
%S A174903 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,
%T A174903 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,
%U A174903 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
%N A174903 Number of divisors d of n such that d<e<2*d for at least another divisor e of n.
%H A174903 Reinhard Zumkeller, <a href="/A174903/b174903.txt">Table of n, a(n) for n = 1..10000</a>
%F A174903 a(A174905(n)) = 0; a(A005279(n)) > 0.
%F A174903 a(A174904(n)) = n and a(m) <> n for m < A174904(n).
%F A174903 a(m)*a(n) <= a(m*n) for m, n coprime.
%e A174903 a(12) = #{(2,3), (3,4), (4,6)} = 3;
%e A174903 a(15) = #{(3,5)} = 1;
%e A174903 a(18) = #{(2,3), (6,9)} = 2;
%e A174903 a(20) = #{(4,5)} = 1;
%e A174903 a(24) = #{(2,3), (3,4), (4,6), (6,8), (8,12)} = 5.
%t A174903 a[n_] := Module[{d = Divisors[n]}, Count[d, _?(Length[Intersection[Range[# + 1, 2*# - 1], d]] > 0 &)]]; Array[a, 100] (* _Amiram Eldar_, Apr 13 2024 *)
%o A174903 (Haskell)
%o A174903 import Data.List (intersect)
%o A174903 a174903 n = length [d | let ds = a027750_row n, d <- ds,
%o A174903                     not $ null [e | e <- [d+1 .. 2*d-1] `intersect` ds]]
%o A174903 -- _Reinhard Zumkeller_, Sep 29 2014
%Y A174903 Cf. A000005, A005279, A174904, A174905.
%K A174903 nonn
%O A174903 1,12
%A A174903 _Reinhard Zumkeller_, Apr 01 2010