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%I #28 Feb 27 2024 04:14:44
%S 1,3,2,7,3,6,4,15,13,9,6,7,7,4,3,31,9,13,10,21,8,18,12,15,31,7,20,14,
%T 15,9,16,63,12,27,2,91,19,10,7,45,21,8,22,21,13,36,24,31,19,93,9,49,
%U 27,20,9,5,20,45,30,21,31,16,26,127,7,36,34,63,24,6,36
%N a(n) = numerator of (sigma(n) / phi(n)).
%H Amiram Eldar, <a href="/A289336/b289336.txt">Table of n, a(n) for n = 1..10000</a>
%H Jean-Marie De Koninck and Florian Luca, <a href="https://eudml.org/doc/284003">On the composition of the Euler function and the sum of divisors function</a>, Colloquium Mathematicum, Vol. 108, No. 1 (2007), pp. 31-51.
%F a(n) = numerator of (A000203(n) / A000010(n)).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A289412(k) = (Pi^4/36) * Product_{p prime} (1 + 2/p^3 - 1/p^5) = 3.6174451656... . - _Amiram Eldar_, Nov 21 2022
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} A289412(k)/a(k) = Product_{p prime} (1 - 3/(p*(p + 1)) + 1/(p^2*(p + 1)) + ((p-1)^3/p^2)*Sum_{k>=3} 1/(p^k-1)) = 0.45782563109026414241... (De Koninck and Luca, 2007). - _Amiram Eldar_, Feb 27 2024
%e Fractions begin with: 1, 3, 2, 7/2, 3/2, 6, 4/3, 15/4, 13/6, 9/2, 6/5, 7, ...
%e For n = 7, sigma(7) / phi(7) = 8/6 = 4/3, a(7) = 4.
%t Array[Numerator[DivisorSigma[1, #]/EulerPhi[#]] &, 71] (* _Michael De Vlieger_, Aug 19 2017 *)
%o (Magma) [Numerator(SumOfDivisors(n) / EulerPhi(n)): n in[1..1000]]
%o (PARI) a(n) = numerator(sigma(n)/eulerphi(n)); \\ _Michel Marcus_, Aug 21 2017
%Y Cf. A289412 (denominators).
%Y Cf. A000010, A000203, A018894, A020492, A023897, A055234, A070032, A070033.
%K nonn,easy,frac
%O 1,2
%A _Jaroslav Krizek_, Aug 19 2017
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