login
Largest number k such that k < d(k)^(n/10), where d(k) is the number of divisors of k.
0

%I #5 May 16 2013 11:25:23

%S 2,2,6,12,12,24,60,180,360,1260,5040,15120,55440,166320,831600,

%T 4324320,36756720,367567200,2327925600,27935107200

%N Largest number k such that k < d(k)^(n/10), where d(k) is the number of divisors of k.

%C Each of these numbers is the product of small primes. For example, a(30) = 2^7 2^3 5^2 7 11 13 17 19. - _T. D. Noe_, May 16 2013

%t Table[last = 0; Do[If[n < DivisorSigma[0,n]^(i/10), last = n], {n, 10^4}]; last, {i, 11, 20}]

%Y Cf. A034884 (n < d(n)^2), A056757 (n < d(n)^3), A225729-A225738.

%K nonn

%O 11,1

%A _T. D. Noe_, May 15 2013