A262618 -id:A262618 - cp's OEIS frontend

A285901 Total number of partitions of all positive integers <= n into an odd number of consecutive parts.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 20, 21, 22, 24, 25, 27, 29, 30, 31, 33, 35, 36, 38, 40, 41, 44, 45, 46, 48, 49, 52, 54, 55, 56, 58, 60, 61, 64, 65, 66, 70, 71, 72, 74, 76, 78, 80, 81, 82, 85, 87, 89, 91, 92, 93, 96, 97, 98, 102, 103, 105, 108, 109, 110, 112, 115, 116, 119, 120, 121, 124, 125, 128, 130

Offset: 1

Omar E. Pol, May 02 2017

nonn

a(n) is also the total number of odd divisors of k less than sqrt(2*k), for k = 1..n.
Conjecture: a(n) is also the total number of subparts present (totally or partially) in an octant of the symmetric representations of sigma of all positive integers <= n.
For more information about the "subparts" of the symmetric representation of sigma see A279387 and A237593.

Partial sums of A082647.

Cf. A001227, A060831, A131576, A196020, A235791, A236104, A237048, A237591, A237593, A244250, A262618, A279387, A285902.

a(n) = A060831(n) - A285902(n).

A262619 Number of parts in the symmetric representation of sigma(n) in two successive octants of two quadrants.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 3, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 1, 1, 3, 5, 1, 1, 1, 1, 1, 3, 1

Offset: 1

Omar E. Pol, Nov 06 2015

nonn

In the diagram of the top view of the pyramid described in A244050 consider a 90-degree sector on two successive octants of two quadrants. The area of the top triangle is equal to 1 and the sum of the areas of all parts (or regions) 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 the mentioned sector of the pyramid.
For more information see A237593 and A237270.

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

Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A244050, A244971, A245092, A262618.

a(n) = A237271(n), if A237271(n) is odd.

a(n) = A237271(n) - 1, if A237271(n) is even.

cp's OEIS Frontend

A285901 Total number of partitions of all positive integers <= n into an odd number of consecutive parts.

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