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%I #13 Sep 08 2022 08:46:23
%S 1,5,3,44,4,5,5,248,45,20,7,22,8,25,2,8213,10,75,11,176,15,35,13,124,
%T 133,40,119,55,16,10,17,2841,7,50,5,330,20,11,12,992,22,25,23,22,30,
%U 65,25,8213,99,665,5,352,28,119,14,62,33,16,31,88,32,85,225
%N a(n) = numerator of Sum_{d|n} (tau(d)/sigma(d)) where tau(k) = the number of the divisors of k (A000005) and sigma(k) = the sum of the divisors of k (A000203).
%C Sum_{d|n} (tau(d)/sigma(d)) >= 1 for all n >= 1.
%F a(p) = (p+3) / gcd(p+3, p+1) for p = primes p.
%e For n=4; Sum_{d|4} (tau(d)/sigma(d)) = (tau(1)/sigma(1))+(tau(2)/sigma(2))+(tau(4)/sigma(4)) = (1/1)+(2/3)+(3/7) = 44/21; a(4) = 44.
%t Array[Numerator@ DivisorSum[#, Divide @@ DivisorSigma[{0, 1}, #] &] &, 63] (* _Michael De Vlieger_, Feb 15 2019 *)
%o (Magma) [Numerator(&+[NumberOfDivisors(d) / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
%o (PARI) a(n) = numerator(sumdiv(n, d, numdiv(d)/sigma(d))); \\ _Michel Marcus_, Feb 13 2019
%Y Cf. A000005, A000203, A323780 (denominator).
%K nonn,frac
%O 1,2
%A _Jaroslav Krizek_, Jan 27 2019
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