A174903 Number of divisors d of n such that d<e<2*d for at least another divisor e of n.

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

1,12

Links

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

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.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000005, A005279, A174904, A174905.

Sequence in context: A186038 A091009 A204814 * A167163 A005890 A104515

Adjacent sequences: A174900 A174901 A174902 * A174904 A174905 A174906

Keyword

nonn,changed

Author

Reinhard Zumkeller, Apr 01 2010

Status

approved