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A322655 Numerator of (Sum_{d|n} sigma(d)) / sigma(n).

%I A322655 #19 May 21 2025 18:45:08
%S A322655 1,4,5,11,7,5,9,26,18,14,13,55,15,3,35,57,19,24,21,11,45,13,25,13,38,
%T A322655 10,29,99,31,35,33,40,65,38,21,198,39,7,75,91,43,15,45,143,21,25,49,
%U A322655 285,22,152,95,165,55,29,91,39,21,62,61,55,63,11,81,247,5,65
%N A322655 Numerator of (Sum_{d|n} sigma(d)) / sigma(n).
%C A322655 Numerator of A007429(n) / A000203(n).
%C A322655 Also numerator of Sum_{d|n} (sigma(d) / sigma(n)).
%H A322655 Antti Karttunen, <a href="/A322655/b322655.txt">Table of n, a(n) for n = 1..20000</a>
%F A322655 a(n) = A007429(n) / gcd(A000203(n), A007429(n)). - _Antti Karttunen_, Nov 15 2021
%e A322655 For n = 4; a(4) = numerator((Sum_{d|4} sigma(d)) / sigma(4)) = numerator((1 + 3 + 7) / (1 + 2 + 4)) = numerator(11/7) = 11.
%t A322655 Table[Numerator[Sum[DivisorSigma[1, d], {d, Divisors[n]}] / DivisorSigma[1, n]], {n, 1, 100}] (* _Vaclav Kotesovec_, Dec 22 2018 *)
%o A322655 (Magma) [Numerator(&+[SumOfDivisors(d): d in Divisors(n)] /  SumOfDivisors(n)): n in [1..1000]];
%o A322655 (PARI) a(n) = numerator(sumdiv(n, d, sigma(d))/sigma(n)); \\ _Michel Marcus_, Dec 22 2018
%Y A322655 Cf. A000203, A007429, A319296, A221219, A322656 (denominator).
%K A322655 nonn,frac
%O A322655 1,2
%A A322655 _Jaroslav Krizek_, Dec 22 2018