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A281007
Number of middle divisors of the n-th number that has middle divisors.
21
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.
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 *)
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 11 2017
STATUS
approved