A347361 Number of widths that are zero in the symmetric representation of sigma(n).

0, 0, 1, 0, 3, 0, 5, 0, 4, 1, 9, 0, 11, 3, 6, 0, 15, 0, 17, 0, 9, 7, 21, 0, 18, 9, 13, 0, 27, 0, 29, 0, 17, 13, 24, 0, 35, 15, 21, 0, 39, 0, 41, 3, 16, 19, 45, 0, 40, 6, 29, 5, 51, 0, 37, 0

Offset: 1

Author

Omar E. Pol, Aug 29 2021

Keywords

• nonn
• more

Comments

a(n) is also the number of columns without ON square cells in the ziggurat diagram of n. Both diagrams can be unified in a three-dimensional version.

a(n) is also the number of zeros 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 widths of the symmetric representation of sigma(n) equals A000203(n).

a(n) = 0, if and only if A237271(n) = 1.

a(p) = p - 2, if p is prime.

For the definition of "width" see A249351.

Crossrefs

Indices of zeros give A174973 and also A238443.

Cf. A000040, A005408, A196020, A235791, A236106, A237270, A237271, A237591, A237593, A249351 (widths), A253258, A347273.

Formula

a(n) = A005408(n-1) - A347273(n).