A262618 Number of parts in the asymmetric representation of sigma(n) in an octant.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1

Offset

1,9

Comments

The diagram of the asymmetric representation of sigma in an octant has been obtained according to the following way: A196020 --> A236104 --> A235791 --> A237591.

Consider that the hypotenuse of the first triangle of the diagram has length 2, so the area of the triangle is equal to 1 and the sum of the areas of all parts added at n-th stage equals sigma(n), the sum of the divisors of n.

a(n) is also the number of terraces at n-th level (starting from the top) in an octant of the step pyramids described in A245092 and A244050.

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000 (computed from the b-file of A237271 provided by Michel Marcus)

Formula

a(n) = (A237271(n) + 1)/2, if A237271(n) is odd.

a(n) = A237271(n)/2, if A237271(n) is even.

Crossrefs

Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A244050, A244971, A245092, A262619.

Sequence in context: A050433 A031263 A204897 * A347447 A107577 A073700

Adjacent sequences: A262615 A262616 A262617 * A262619 A262620 A262621

Keyword

nonn

Author

Omar E. Pol, Nov 05 2015

Status

approved