A323780 - OEIS

%I #10 Sep 08 2022 08:46:23

%S 1,3,2,21,3,2,4,105,26,9,6,7,7,12,1,3255,9,26,10,63,8,18,12,35,93,21,

%T 65,21,15,3,16,1085,4,27,3,91,19,6,7,315,21,8,22,9,13,36,24,2170,76,

%U 279,3,147,27,39,9,21,20,9,30,21,31,48,104,137795,21,12,34

%N a(n) = denominator 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+1) / gcd(p+3, p+1) for p = primes p.

%F a(n) = 1 for numbers in A323781.

%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) = 21.

%t Array[Denominator@ DivisorSum[#, Divide @@ DivisorSigma[{0, 1}, #] &] &, 67] (* _Michael De Vlieger_, Feb 15 2019 *)

%o (Magma) [Denominator(&+[NumberOfDivisors(d) / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]

%o (PARI) a(n) = denominator(sumdiv(n, d, numdiv(d)/sigma(d))); \\ _Michel Marcus_, Feb 13 2019

%Y Cf. A000005, A000203, A323779 (numerator), A323781.

%K nonn,frac

%O 1,2

%A _Jaroslav Krizek_, Feb 13 2019