A317582 a(n) is the number of k with 1 <= k <= n-1 such that a(k) * a(n-k) <= n.

0, 1, 2, 3, 4, 5, 6, 6, 4, 4, 4, 6, 8, 8, 8, 8, 6, 7, 8, 9, 10, 9, 6, 6, 6, 8, 10, 14, 12, 12, 10, 8, 10, 12, 14, 14, 14, 8, 6, 10, 12, 18, 16, 14, 12, 9, 12, 15, 20, 21, 18, 16, 8, 12, 18, 20, 16, 16, 14, 14, 14, 14, 20, 23, 18, 16, 16, 14, 18, 22, 22, 22, 16

Offset

1,3

Comments

This sequence can be described as a(n) = Sum_{k=1..n-1} [Q(a(k), a(n-k), n] for some predicate Q in three variables, one of which corresponds to n; in that sense, this is a generalization of the sequences described in A317420.

See A317596 and A317638 for similar sequences.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

For n = 9:
- a(1) * a(8) = 0 * 6 = 0 <= 9,
- a(2) * a(7) = 1 * 6 = 6 <= 9,
- a(3) * a(6) = 2 * 5 = 10 > 9,
- a(4) * a(5) = 3 * 4 = 12 > 9,
- a(5) * a(4) = 4 * 3 = 12 > 9,
- a(6) * a(3) = 5 * 2 = 10 > 9,
- a(7) * a(2) = 6 * 1 = 6 <= 9,
- a(8) * a(1) = 6 * 0 = 0 <= 9,
- hence a(9) = 4.

Prog

(PARI) a = vector(73); for (n=1, #a, a[n] = sum(k=1, n-1, a[k]*a[n-k] <= n); print1 (a[n] ", "))

Crossrefs

Cf. A317420, A317596, A317638.

Sequence in context: A239132 A307311 A272081 * A293705 A036055 A034151

Adjacent sequences: A317579 A317580 A317581 * A317583 A317584 A317585

Keyword

nonn

Author

Rémy Sigrist, Aug 01 2018

Status

approved