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 A323761 Denominator of Product_{d|n} (pod(d)/tau(d)) where pod(k) = the product of the divisors of k and tau(k) = the number of the divisors of k. 3
 1, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 16, 15, 2, 1, 2, 9, 16, 2, 2, 1, 6, 2, 8, 9, 2, 8, 2, 45, 16, 2, 16, 1, 2, 2, 16, 9, 2, 8, 2, 9, 32, 2, 2, 25, 6, 9, 16, 9, 2, 1, 16, 9, 16, 2, 2, 1, 2, 2, 32, 315, 16, 8, 2, 9, 16, 8, 2, 1, 2, 2, 32, 9, 16, 8, 2, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2. LINKS FORMULA a(p) = 2 for prime p > 2. a(n) = 1 for numbers in A323762. EXAMPLE For n=4; Product_{d|4} (pod(d)/tau(d)) = (pod(1)/tau(1))*(pod(2)/tau(2))*(pod(4)/tau(4)) = (1/1)*(2/2)*(8/3) = 8/3; a(4) = 3. MAPLE A323761 := proc(n)     denom(A266265(n)/A211776(n)) ; end proc: seq(A323761(n), n=1..20) ; # R. J. Mathar, Feb 13 2019 PROG (MAGMA) [Denominator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]] (PARI) a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); denominator(p); \\ Michel Marcus, Jan 27 2019 CROSSREFS Cf. A211776, A266265, A323760 (numerator), A323762. Sequence in context: A208243 A209320 A097051 * A078832 A086410 A185049 Adjacent sequences:  A323758 A323759 A323760 * A323762 A323763 A323764 KEYWORD nonn,frac AUTHOR Jaroslav Krizek, Jan 27 2019 STATUS approved

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Last modified June 26 00:10 EDT 2019. Contains 324367 sequences. (Running on oeis4.)