A285902 Total number of partitions of all positive integers <= n into an even number of consecutive parts.

0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 14, 15, 16, 16, 17, 18, 20, 20, 21, 22, 23, 23, 25, 26, 27, 28, 29, 30, 32, 32, 33, 34, 35, 36, 38, 39, 40, 40, 41, 42, 44, 45, 46, 47, 49, 49, 51, 52, 53, 54, 55, 56, 58, 58, 60, 61, 62, 63, 65, 66, 67, 67, 68, 69, 72, 73, 74, 76, 77, 77, 79, 80, 81, 82

Offset

1,5

Comments

a(n) is also the total number of odd divisors of k greater than sqrt(2*k), for k = 1..n.

Conjecture: a(n) is also the total number of pairs of equidistant subparts of all 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..84.

Formula

a(n) = A060831(n) - A285901(n).

Crossrefs

Partial sums of A131576.

Cf. A001227, A060831, A082647, A196020, A235791, A236104, A237048, A237270, A237591, A237593, A237270, A279387, A245092, A262626, A285901.

Sequence in context: A346693 A265436 A060151 * A097330 A086861 A113865

Adjacent sequences: A285899 A285900 A285901 * A285903 A285904 A285905

Keyword

nonn

Author

Omar E. Pol, May 02 2017

Status

approved