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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.

%I A323761 #14 Sep 08 2022 08:46:23
%S A323761 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,
%T A323761 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,
%U A323761 32,315,16,8,2,9,16,8,2,1,2,2,32,9,16,8,2,9
%N 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.
%C A323761 Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.
%H A323761 Antti Karttunen, <a href="/A323761/b323761.txt">Table of n, a(n) for n = 1..20000</a>
%F A323761 a(p) = 2 for prime p > 2.
%F A323761 a(n) = 1 for numbers in A323762.
%e A323761 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.
%p A323761 A323761 := proc(n)
%p A323761     denom(A266265(n)/A211776(n)) ;
%p A323761 end proc:
%p A323761 seq(A323761(n),n=1..20) ; # _R. J. Mathar_, Feb 13 2019
%o A323761 (Magma) [Denominator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o A323761 (PARI) a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); denominator(p); \\ _Michel Marcus_, Jan 27 2019
%Y A323761 Cf. A211776, A266265, A323760 (numerator), A323762.
%K A323761 nonn,frac
%O A323761 1,3
%A A323761 _Jaroslav Krizek_, Jan 27 2019