A365195 Height of the first staircase of the ziggurat of order n described in A347186.

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

Offset

1,2

Comments

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.

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

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

From Omar E. Pol, Oct 22 2023: (Start)

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

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

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

Links

Table of n, a(n) for n=1..80.

Formula

a(n) <= n.

a(2*n-1) = n.

Crossrefs

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

Sequence in context: A343327 A060766 A321015 * A365433 A029578 A054345

Adjacent sequences: A365192 A365193 A365194 * A365196 A365197 A365198

Keyword

nonn

Author

Omar E. Pol, Aug 25 2023

Extensions

More terms from Omar E. Pol, Oct 22 2023

Status

approved