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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..78.

Formula

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

Crossrefs

Partial sums of A082647.

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

Sequence in context: A107750 A196736 A284946 * A246716 A362618 A371782

Adjacent sequences: A285898 A285899 A285900 * A285902 A285903 A285904

Keyword

nonn

Author

Omar E. Pol, May 02 2017

Status

approved