A078632 Number of geometric subsequences of [1,...,n] with integral successive-term ratio and length > 1.

0, 1, 2, 5, 6, 9, 10, 15, 18, 21, 22, 28, 29, 32, 35, 43, 44, 50, 51, 57, 60, 63, 64, 73, 76, 79, 84, 90, 91, 98, 99, 109, 112, 115, 118, 129, 130, 133, 136, 145, 146, 153, 154, 160, 166, 169, 170, 183, 186, 192, 195, 201, 202, 211, 214, 223, 226, 229, 230, 242

Offset

1,3

Comments

The number of geometric subsequences of [1,...,n] with integral successive-term ratio r and length k is floor(n/r^(k-1))(n > 0, r > 1, k > 0).

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = sum {r > 1, j > 0} floor(n/r^j)

Example

a(2): [1,2]; a(3): [1,2],[1,3]; a(4): [1,2],[1,3],[1,4],[2,4],[1,2,4]

Crossrefs

Cf. A078651.

Sequence in context: A373226 A213730 A191172 * A309242 A122701 A032925

Adjacent sequences: A078629 A078630 A078631 * A078633 A078634 A078635

Keyword

nonn,easy

Author

Robert E. Sawyer (rs.1(AT)mindspring.com)

Status

approved