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A323760 Numerator 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 A323760 #11 Sep 08 2022 08:46:23
%S A323760 1,1,3,8,5,27,7,128,27,125,11,10368,13,343,3375,131072,17,118098,19,
%T A323760 2000000,9261,1331,23,6879707136,625,2197,19683,15059072,29,
%U A323760 38443359375,31,2147483648,35937,4913,42875,101559956668416,37,6859,59319,10240000000000,41
%N A323760 Numerator 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 A323760 Product_{d|n} (pod(d)/tau(d)) > 1 for all n > 2.
%F A323760 a(p) = p for primes p > 2.
%e A323760 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) = 8.
%p A323760 A323760 := proc(n)
%p A323760     numer(A266265(n)/A211776(n)) ;
%p A323760 end proc:
%p A323760 seq(A323760(n),n=1..20) ; # _R. J. Mathar_, Feb 13 2019
%o A323760 (Magma) [Numerator(&*[&*[c: c in Divisors(d)] / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o A323760 (PARI) a(n) = my(p=1, vd); fordiv(n, d, vd = divisors(d); p *= vecprod(vd)/#vd); numerator(p); \\ _Michel Marcus_, Jan 27 2019
%Y A323760 Cf. A211776, A266265, A323761 (denominator).
%K A323760 nonn,frac
%O A323760 1,3
%A A323760 _Jaroslav Krizek_, Jan 26 2019