A281007 Number of middle divisors of the n-th number that has middle divisors.

1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 4, 1, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 4, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 4, 1, 2, 4, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2

Offset

1,4

Comments

Conjecture 1: also widths of the successive terraces that we can find descending by the main diagonal of the pyramid described in A245092. Hence, bisection of A281012.

Conjecture 2: also number of central subparts in the symmetric representation of sigma of the numbers j that have the property that the number of parts in the symmetric representation of sigma(j) is odd.

Conjecture 3: Partial sums give A282131.

Links

Table of n, a(n) for n=1..105.

Formula

a(n) = A067742(A071562(n)).

Mathematica

DeleteCases[#, 0] &@ Table[Count[Divisors@ n, d_ /; Sqrt[n/2] <= d < Sqrt[2 n]], {n, 300}] (* Michael De Vlieger, Feb 12 2017 *)

Crossrefs

Positive terms in A067742.

Cf. A071562, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A240542, A244050, A244367, A244580, A245092, A262626, A279387, A280919, A281012, A282131.

Sequence in context: A160245 A154351 A112753 * A023589 A134034 A174886

Adjacent sequences: A281004 A281005 A281006 * A281008 A281009 A281010

Keyword

nonn

Author

Omar E. Pol, Feb 11 2017

Status

approved