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%I #23 Sep 08 2022 08:46:25
%S 1,2,2,36,2,16,2,864,36,16,2,10368,2,16,16,6480000,2,10368,2,10368,16,
%T 16,2,11943936,36,16,864,10368,2,4096,2,64800000,16,16,16,2176782336,
%U 2,16,16,11943936,2,4096,2,10368,10368,16,2,1343692800000000,36,10368,16
%N a(n) = Product_{d|n} (A253139(n) / tau(d)) where A253139(n) = lcm_{d|n} tau(d).
%F a(n) = ((lcm_{d|n} tau(d))^tau(n)) / Product_{d|n} tau(d).
%F a(n) = A253139(n)^A000005(n) / A211776(n).
%F a(p) = 2 for p = primes (A000040).
%F a(n) = 2^(k*2^(k-1)) if n is a product of k distinct primes.
%e For n = 6; divisors d of 6: {1, 2, 3, 6}; tau(d): {1, 2, 2, 4}; lcm_{d|6} tau(d) = 4; a(6) = 4/1 * 4/2 * 4/2 * 4/4 = 16.
%t a[n_] := (LCM @@ (s = DivisorSigma[0, Divisors[n]]))^Length[s] / Times @@ s; Array[a, 51] (* _Amiram Eldar_, May 02 2020 *)
%o (Magma) [&*[ LCM([#Divisors(d): d in Divisors(n)]) / #Divisors(d): d in Divisors(n)]: n in [1..100]]
%o (PARI) a(n) = {my(d=divisors(n), lcmd = lcm(vector(#d, k, numdiv(d[k])))); vecprod(vector(#d, k, lcmd/numdiv(d[k])));} \\ _Michel Marcus_, May 02 2020
%Y Cf. A334471 (similar sequence with sigma(d)).
%Y Cf. A000005, A000040, A211776, A253139.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, May 01 2020
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