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 A334470 a(n) = Product_{d|n} (A253139(n) / tau(d)) where A253139(n) = lcm_{d|n} tau(d). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..51. FORMULA a(n) = ((lcm_{d|n} tau(d))^tau(n)) / Product_{d|n} tau(d). a(n) = A253139(n)^A000005(n) / A211776(n). a(p) = 2 for p = primes (A000040). a(n) = 2^(k*2^(k-1)) if n is a product of k distinct primes. EXAMPLE 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. MATHEMATICA a[n_] := (LCM @@ (s = DivisorSigma[0, Divisors[n]]))^Length[s] / Times @@ s; Array[a, 51] (* Amiram Eldar, May 02 2020 *) PROG (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 CROSSREFS Cf. A334471 (similar sequence with sigma(d)). Cf. A000005, A000040, A211776, A253139. Sequence in context: A297795 A024176 A349033 * A286375 A056612 A131658 Adjacent sequences: A334467 A334468 A334469 * A334471 A334472 A334473 KEYWORD nonn AUTHOR Jaroslav Krizek, May 01 2020 STATUS approved

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Last modified June 8 04:57 EDT 2023. Contains 363157 sequences. (Running on oeis4.)