A056795 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.