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

Author

Omar E. Pol, May 02 2017

Keywords

• nonn

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.

Crossrefs

Partial sums of A082647.

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

Formula

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