A056795 Number of divisors of k as k runs through sequence of distinct values of LCM(1,..,n).

1, 2, 4, 6, 12, 24, 32, 48, 96, 192, 240, 480, 960, 1920, 2880, 3840, 7680, 15360, 18432, 36864, 73728, 147456, 294912, 442368, 884736, 1769472, 3538944, 4128768, 8257536, 16515072, 33030144, 66060288, 82575360, 165150720, 330301440

Offset: 1

Author

Labos Elemer, Aug 28 2000

Keywords

• nonn

Comments

Values of LCM's in A003418 and accordingly their number of divisors jump at powers of primes (A000961). Here divisor-numbers of LCM's are displayed without repetition.

Examples

			For x = 19,20,21,22 the value of A003418(x) = A051451(13) = LCM(1,..,x) = 232792560, of which the total number of divisors is 960, so a(13) = 960.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3365

Crossrefs

Cf. A000005, A003418, A051451, A000961.

Partial sums of A305215.

Programs

PARI

f(n) = lcm(vector(n, i, i)); \\ A003418
lista(nn) = {my(last = 0); for (n=1, nn, my(new = f(n)); if (new != last, print1(numdiv(new), ", "); last = new););} \\ Michel Marcus, Oct 08 2020

Formula

a(n) = A000005(A051451(n)).