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A334470
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a(n) = Product_{d|n} (A253139(n) / tau(d)) where A253139(n) = lcm_{d|n} tau(d).
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2
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1, 2, 2, 36, 2, 16, 2, 864, 36, 16, 2, 10368, 2, 16, 16, 6480000, 2, 10368, 2, 10368, 16, 16, 2, 11943936, 36, 16, 864, 10368, 2, 4096, 2, 64800000, 16, 16, 16, 2176782336, 2, 16, 16, 11943936, 2, 4096, 2, 10368, 10368, 16, 2, 1343692800000000, 36, 10368, 16
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = ((lcm_{d|n} tau(d))^tau(n)) / Product_{d|n} tau(d).
a(n) = 2^(k*2^(k-1)) if n is a product of k distinct primes.
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := (LCM @@ (s = DivisorSigma[0, Divisors[n]]))^Length[s] / Times @@ s; Array[a, 51] (* Amiram Eldar, May 02 2020 *)
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PROG
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(Magma) [&*[ LCM([#Divisors(d): d in Divisors(n)]) / #Divisors(d): d in Divisors(n)]: n in [1..100]]
(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
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CROSSREFS
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Cf. A334471 (similar sequence with sigma(d)).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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