

A285901


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


6



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
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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 A319161
Adjacent sequences: A285898 A285899 A285900 * A285902 A285903 A285904


KEYWORD

nonn


AUTHOR

Omar E. Pol, May 02 2017


STATUS

approved



