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

Author

Omar E. Pol, May 02 2017

Keywords

• nonn

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.

Crossrefs

Partial sums of A131576.

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

Formula

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