A101207 For each prime power n, a(n) is the number of positive integers that have n as their greatest prime power.

1, 1, 2, 2, 6, 0, 12, 8, 16, 0, 48, 0, 96, 0, 0, 48, 240, 0, 480, 0, 0, 0, 960, 0, 960, 0, 960, 0, 3840, 0, 7680, 3072, 0, 0, 0, 0, 18432, 0, 0, 0, 36864, 0, 73728, 0, 0, 0, 147456, 0, 147456, 0, 0, 0, 442368, 0, 0, 0, 0, 0, 884736, 0, 1769472, 0, 0, 589824

Offset

1,3

Comments

a(n) is the number of occurrences of n in A034699.

Links

Table of n, a(n) for n=1..64.

Formula

a(1) = 1; a(p^k) = prod_{q <= p^k, q prime} { ceiling(k log p / log q) } / k when p prime, k >= 1, a(n) = 0 otherwise

Example

a(4) = 2 since only 4 and 12 have 4 as their greatest prime power - all other multiples of 4 are divisible by 8, 9, or some prime >= 5.

Crossrefs

Cf. A034699.

Sequence in context: A274440 A199220 A047916 * A186435 A260297 A199476

Adjacent sequences: A101204 A101205 A101206 * A101208 A101209 A101210

Keyword

nonn,easy

Author

Hugo van der Sanden, Dec 13 2004

Status

approved