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

Author

Omar E. Pol, Aug 29 2021

Keywords

• nonn
• more

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.

Crossrefs

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

Formula

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