A307892 - OEIS

%I #16 Sep 23 2024 10:13:56

%S 1,1,2,6,2,6,2,8,3,10,2,144,2,14,60,320,2,324,2,1200,84,22,2,13824,15,

%T 26,108,2352,2,27000,2,3072,132,34,140,279936,2,38,156,64000,2,74088,

%U 2,5808,4050,46,2,26542080,21,7500,204,8112,2,157464,220,175616,228

%N a(n) = lcm(tau(n), pod(n)) / n, where tau(k) = the number of divisors of k (A000005) and pod(n) = the product of divisors of k (A007955).

%C n divides lcm(tau(n), pod(n)) for all n >= 1.

%H Harvey P. Dale, <a href="/A307892/b307892.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A324528(n) / n.

%e For n=4: a(4) = lcm(tau(4), pod(4))/4 = lcm(3, 8)/4 = 24/4 = 6.

%t Table[(LCM[DivisorSigma[0,n],Times@@Divisors[n]])/n,{n,60}] (* _Harvey P. Dale_, Sep 22 2024 *)

%o (Magma) [LCM(NumberOfDivisors(n), &*[d: d in Divisors(n)]) / n: n in [1.. 10^5]];

%Y Cf. A000005, A007955, A324528.

%K nonn

%O 1,3

%A _Jaroslav Krizek_, May 03 2019