A365195 - OEIS

%I #59 Oct 22 2023 22:58:47

%S 1,2,2,4,3,6,4,8,5,9,6,12,7,12,8,16,9,18,10,20,11,18,12,24,13,21,14,

%T 28,15,30,16,32,17,27,18,36,19,30,20,40,21,42,22,42,23,36,24,48,25,39,

%U 26,49,27,54,28,56,29,45,30,60,31,48,32,64,33,66,34,63,35,54,36,72,37,57,38,70,39,77,40,80

%N Height of the first staircase of the ziggurat of order n described in A347186.

%C a(n) is also the number of square cells in the first layer of the symmetric representation of sigma(n) from the border to, at most, the axis of symmetry of the diagram.

%C The values of a(n) where a(n) = n give A174973.

%C Since this is a supersequence of A174973 so all powers of 2 and all even perfect numbers are in the sequence.

%C From _Omar E. Pol_, Oct 22 2023: (Start)

%C The values of a(n) where a(n) is not equal to n give A238524.

%C If n is an odd prime then a(n) = (n + 1)/2.

%C Shares infinitely many terms with A365433 from which first differs at a(15). (End)

%F a(n) <= n.

%F a(2*n-1) = n.

%Y Cf. A000079, A000396, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238524, A262626, A279387, A347186, A347367, A365433, A365434.

%K nonn

%O 1,2

%A _Omar E. Pol_, Aug 25 2023

%E More terms from _Omar E. Pol_, Oct 22 2023