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a(n) = lcm(sigma(n), pod(n)) / n, where sigma (k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).
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%I #10 May 29 2024 12:41:27

%S 1,3,4,14,6,6,8,120,39,90,12,1008,14,84,120,1984,18,4212,20,8400,672,

%T 198,24,69120,155,546,1080,784,30,27000,32,64512,528,918,1680,

%U 25474176,38,570,2184,576000,42,148176,44,40656,52650,828,48,164560896,399,232500

%N a(n) = lcm(sigma(n), pod(n)) / n, where sigma (k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).

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

%F a(n) = A324529(n) / n.

%e For n=4: a(4) = lcm(sigma(4), pod(4))/4 = lcm(7, 8)/4 = 56/4 = 14.

%t Table[LCM[DivisorSigma[1,n],Times@@Divisors[n]]/n,{n,60}] (* _Harvey P. Dale_, May 29 2024 *)

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

%Y Cf. A000203, A007955, A324529.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, May 03 2019