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

1,5

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.

Links

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

Formula

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

Crossrefs

Indices of zeros give A174973 and also A238443.

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

Sequence in context: A058026 A004605 A369700 * A175919 A086664 A164736

Adjacent sequences: A347358 A347359 A347360 * A347362 A347363 A347364

Keyword

nonn,more

Author

Omar E. Pol, Aug 29 2021

Status

approved