A347273 Number of positive widths in the symmetric representation of sigma(n).

1, 3, 4, 7, 6, 11, 8, 15, 13, 18, 12, 23, 14, 24, 23, 31, 18, 35, 20, 39, 32, 36, 24, 47, 31, 42, 40, 55, 30, 59, 32, 63, 48, 54, 45, 71, 38, 60, 56, 79, 42, 83, 44, 84, 73, 72, 48, 95, 57, 93, 72, 98, 54, 107, 72, 111

Offset

1,2

Comments

a(n) is also the number of columns that contain ON cells in the ziggurat diagram of n. Both diagrams can be unified in a three-dimensional version.

a(n) is also the number of nonzero terms in the n-th row of A249351.

The number of widths in the symmetric representation of sigma(n) is equal to 2*n - 1 = A005408(n-1).

The sum of the positive widths (also the sum of all widths) of the symmetric representation of sigma(n) equals A000203(n).

Indices where a(n) = 2*n - 1 give A174973 and also A238443.

a(p) = p + 1, if p is prime.

a(n) = 2*n - 1, if and only if A237271(n) = 1.

a(n) = A000203(n) if n is a member of A174905.

For the definition of "width" see A249351.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = A005408(n-1) - A347361(n).

Crossrefs

Cf. A000040, A005408, A174905, A174973, A196020, A235791, A236106, A237270, A237271, A237591, A237593, A238443, A249351 (widths), A253258, A347361.

Sequence in context: A347529 A279388 A292288 * A355584 A113957 A366148

Adjacent sequences: A347270 A347271 A347272 * A347274 A347275 A347276

Keyword

nonn,more

Author

Omar E. Pol, Aug 29 2021

Status

approved