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A285901 Total number of partitions of all positive integers <= n into an odd number of consecutive parts. 5
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 (list; graph; refs; listen; history; text; internal format)
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 A212165 A130091

Adjacent sequences:  A285898 A285899 A285900 * A285902 A285903 A285904

KEYWORD

nonn

AUTHOR

Omar E. Pol, May 02 2017

STATUS

approved

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Last modified August 16 21:46 EDT 2018. Contains 313809 sequences. (Running on oeis4.)