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%I #11 Sep 08 2022 08:46:23
%S 1,1,3,8,5,9,7,16,9,25,11,32,13,49,225,1024,17,972,19,4000,441,121,23,
%T 41472,125,169,729,10976,29,101250,31,16384,1089,289,1225,1119744,37,
%U 361,1521,320000,41,388962,43,42592,30375,529,47,127401984,343,62500,2601
%N a(n) = denominator of Sum_{d|n} tau(d)/pod(d) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
%C Sum_{d|n} tau(d)/pod(d) > 1 for all n > 1.
%F a(n) = 1 for n = 1, 2, ... (no other n <= 5*10^6).
%F a(p) = p for prime p > 2.
%e For n=4; Sum_{d|4} tau(d)/pod(d) = tau(1)/pod(1) + tau(2)/pod(2) + tau(4)/pod(4) = 1/1 + 2/2 + 3/8 = 19/8; a(4) = 8.
%t Array[Denominator@ DivisorSum[#, DivisorSigma[0, #]/Apply[Times, Divisors@ #] &] &, 51] (* _Michael De Vlieger_, Jan 27 2019 *)
%o (Magma) [Denominator(&+[NumberOfDivisors(d) / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = denominator(sumdiv(n, d, numdiv(d)/vecprod(divisors(d)))); \\ _Michel Marcus_, Jan 26 2019
%Y Cf. A000005, A007955, A323706 (numerator).
%K nonn,frac
%O 1,3
%A _Jaroslav Krizek_, Jan 26 2019