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A285901
Total number of partitions of all positive integers <= n into an odd number of consecutive parts.
10
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
1,2
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.
FORMULA
a(n) = A060831(n) - A285902(n).
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 02 2017
STATUS
approved