login
Number of divisors of k as k runs through sequence of distinct values of LCM(1,..,n).
2

%I #16 Oct 10 2020 05:53:19

%S 1,2,4,6,12,24,32,48,96,192,240,480,960,1920,2880,3840,7680,15360,

%T 18432,36864,73728,147456,294912,442368,884736,1769472,3538944,

%U 4128768,8257536,16515072,33030144,66060288,82575360,165150720,330301440

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

%C 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.

%H Amiram Eldar, <a href="/A056795/b056795.txt">Table of n, a(n) for n = 1..3365</a>

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

%e 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.

%o (PARI) f(n) = lcm(vector(n, i, i)); \\ A003418

%o 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

%Y Cf. A000005, A003418, A051451, A000961.

%Y Partial sums of A305215.

%K nonn

%O 1,2

%A _Labos Elemer_, Aug 28 2000