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

1,2

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.

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A000005, A003418, A051451, A000961.

Partial sums of A305215.

Sequence in context: A368252 A378133 A095416 * A141420 A141551 A181804

Adjacent sequences: A056792 A056793 A056794 * A056796 A056797 A056798

Keyword

nonn

Author

Labos Elemer, Aug 28 2000

Status

approved