A274919 Sum of all perimeters of all parts of the symmetric representation of sigma(n).

4, 8, 12, 16, 16, 24, 20, 32, 32, 40, 28, 48, 32, 52, 52, 64, 40, 72, 44, 80, 72, 76, 52, 96, 68, 88, 88, 112, 64, 120, 68, 128

Offset: 1

Author

Omar E. Pol, Dec 11 2016

Keywords

• nonn
• more

Comments

a(n) is also the number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of sigma in two quadrants (without the axis x and y).

Examples

			Illustration of a(9) = 32:
.         12
.     _ _ _ _ _
.    |_ _ _ _ _|
.               _ _ 8
.              |_  |
.                |_|  _
.                    | |
.                    | |
.                    | |  12
.                    | |
.                    |_|
.
For n = 9 the symmetric representation of sigma(9) = 13 has three parts of areas 5, 3, 5 respectively. The perímeters of the parts are 12, 8 and 12 as shown above. The sum of the perimeters is 12 + 8 + 12 = 32, so a(9) = 32.
		

Crossrefs

Cf. A000203, A008586, A196020, A236104, A237270, A237271, A237593, A244361, A244363, A244370, A244371, A245092, A262626, A279228.

Formula

a(n) = 4*A244361(n) = 2*A244363(n) = A244371(n)/2.

a(n) = A008586(n) - 2*A279228(n). - Omar E. Pol, May 04 2023

Extensions

a(29)-a(32) from Omar E. Pol, May 04 2023