|
%I #29 Oct 17 2023 07:39:27
%S 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,
%T 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,
%U 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
%N Number of middle divisors of the n-th number whose divisors increase by a factor of 2 or less.
%C The middle divisors of n are the divisors in the half-open interval [sqrt(n/2), sqrt(n*2)).
%C 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.
%C For the diagrams related to the first 13 terms of this sequence see A317305.
%F a(n) = A067742(A174973(n)).
%t 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 *)
%Y Cf. A067742, A174973, A237048, A237270, A237593, A281007, A317305, A354452.
%K nonn
%O 1,4
%A _Omar E. Pol_, Mar 06 2023
|
