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A361208
Number of middle divisors of the n-th number whose divisors increase by a factor of 2 or less.
1
1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 1, 2, 2, 2, 4, 2, 1, 2, 2, 3, 2, 2, 2, 1, 2, 2, 4, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 4, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 1, 2, 3, 2, 2, 2, 4, 4, 2, 2, 3, 2, 2, 2, 2, 2, 2, 4
OFFSET
1,4
COMMENTS
The middle divisors of n are the divisors in the half-open interval [sqrt(n/2), sqrt(n*2)).
Also consider the n-th number k with the property that the symmetric representation of sigma(k) has only one part. a(n) is the number of square cells on the axis of symmetry of the diagram.
For the diagrams related to the first 13 terms of this sequence see A317305.
FORMULA
a(n) = A067742(A174973(n)).
MATHEMATICA
With[{$MaxExtraPrecision = 1000}, Map[Function[n, Count[Divisors[n], _?(Sqrt[n/2] <= # < Sqrt[2 n] &)]], Select[Range[500], And @@ Map[# <= 2 &, (Rest[#]/Most[#])] &@ Divisors[#] &]] ] (* Michael De Vlieger, Mar 28 2023, after Harvey P. Dale at A174973 *)
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 06 2023
STATUS
approved