A243224 Number of odd divisors d of n such that d > 1 and d(1+d/3)/2 <= n <= 3d(d-1)/2.

0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0

Offset

1,45

Comments

This sequence is useful for computing A243223, the number of partitions of n into summands in arithmetic progression with common difference 3. The definition follows Nyblom and Evans 2003 (see LINK) with slight modifications and corrections.

Links

Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

M. A. Nyblom and C. Evans, On the enumeration of partitions with summands in arithmetic progression, Australasian Journal of Combinatorics, Vol. 28 (2003), pp. 149-159.

Example

a(6) = 1 because 3, the unique odd divisor > 1 of 6 satisfies 3(1+3/3)/2 <= 6 <= 3.3(3-1)/2.

Prog

(PARI) a(n) = sumdiv(n, d, (d > 1) && (d % 2) && (d*(1+d/3)/2 <= n) && (n <= 3*d*(d-1)/2)); \\ Michel Marcus, Jun 02 2014

Crossrefs

Cf. A243223.

Sequence in context: A316717 A328831 A085981 * A127324 A083917 A117974

Adjacent sequences: A243221 A243222 A243223 * A243225 A243226 A243227

Keyword

nonn

Author

Jean-Christophe Hervé, Jun 01 2014

Status

approved