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A276737 a(n) = denominator of Sum_{d|n} tau(d)/d.

%I A276737 #19 Sep 08 2022 08:46:17
%S A276737 1,1,3,4,5,3,7,4,1,5,11,12,13,7,3,16,17,1,19,20,7,11,23,12,25,13,27,
%T A276737 28,29,3,31,4,33,17,5,2,37,19,13,20,41,7,43,4,5,23,47,16,49,25,51,52,
%U A276737 53,27,55,28,19,29,59,12,61,31,7,64,13,33,67,68,69,5,71
%N A276737 a(n) = denominator of Sum_{d|n} tau(d)/d.
%C A276737 Also denominator of (Sum_{d|n} sigma(d)) / n.
%H A276737 Jaroslav Krizek, <a href="/A276737/b276737.txt">Table of n, a(n) for n = 1..1000</a>
%F A276737 a(A068978(n)) = 1.
%F A276737 For all n, n = (Sum_{d|n} sigma(d)) / (Sum_{d|n} tau(d)/d) = (Sum_{d|n} d*tau(n/d)) / (Sum_{d|n} tau(d)/d) = A007429(n) * a(n) / A276736(n).
%e A276737 For n=6; {d_6} = {1, 2, 3, 6}; {tau(d)_6} = {1, 2, 2, 4}; Sum_{d|6} tau(d)/d = 1/1 + 2/2 + 2/3 + 4/6 = 20/6 = 10/3; a(6) = 3.
%e A276737 For n=6; {d_6} = {1, 2, 3, 6}; {sigma(d)_6} = {1, 3, 4, 12};  (Sum_{d|6} sigma(d))/6 = (1+3+4+12)/6 = 10/3; a(6) = 3.
%t A276737 Table[Denominator@ Total[DivisorSigma[0, #]/#] &@ Divisors@ n, {n, 71}] (* _Michael De Vlieger_, Sep 16 2016 *)
%o A276737 (Magma) [Denominator(&+[NumberOfDivisors(d)/d: d in Divisors(n)]): n in [1..100]]
%o A276737 (PARI) a(n) = denominator(sumdiv(n, d, numdiv(d)/d)); \\ _Michel Marcus_, Sep 16 2016
%Y A276737 Cf. A000005, A007429, A068978, A276736 (numerators).
%K A276737 nonn,frac
%O A276737 1,3
%A A276737 _Jaroslav Krizek_, Sep 16 2016