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

Author

Hugo van der Sanden, Dec 13 2004

Keywords

• nonn
• easy

Comments

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

Examples

			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.

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