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A322656 Denominator of (Sum_{d|n} sigma(d)) / sigma(n).

%I A322656 #18 May 21 2025 18:45:59
%S A322656 1,3,4,7,6,3,8,15,13,9,12,28,14,2,24,31,18,13,20,6,32,9,24,6,31,7,20,
%T A322656 56,30,18,32,21,48,27,16,91,38,5,56,45,42,8,44,84,13,18,48,124,19,93,
%U A322656 72,98,54,15,72,20,16,45,60,24,62,8,52,127,4,36,68,126,96
%N A322656 Denominator of (Sum_{d|n} sigma(d)) / sigma(n).
%C A322656 Denominator of A007429(n) / A000203(n).
%C A322656 Also denominator of Sum_{d|n} (sigma(d) / sigma(n)).
%H A322656 Antti Karttunen, <a href="/A322656/b322656.txt">Table of n, a(n) for n = 1..20000</a>
%F A322656 a(n) = 1 for numbers in A221219.
%F A322656 a(n) = A000203(n) / gcd(A000203(n), A007429(n)). - _Antti Karttunen_, Nov 15 2021
%e A322656 For n = 4; a(4) = denominator((Sum_{d|4} sigma(d)) / sigma(4)) = denominator((1 + 3 + 7) / (1 + 2 + 4)) = denominator(11/7) = 7.
%t A322656 Table[Denominator[Sum[DivisorSigma[1, d], {d, Divisors[n]}] / DivisorSigma[1, n]], {n, 1, 100}] (* _Vaclav Kotesovec_, Dec 22 2018 *)
%o A322656 (Magma) [Denominator(&+[SumOfDivisors(d): d in Divisors(n)] /  SumOfDivisors(n)): n in [1..1000]];
%o A322656 (PARI) a(n) = denominator(sumdiv(n, d, sigma(d))/sigma(n)); \\ _Michel Marcus_, Dec 22 2018
%Y A322656 Cf. A000203, A007429, A319296, A221219, A322655 (numerator).
%K A322656 nonn,frac
%O A322656 1,2
%A A322656 _Jaroslav Krizek_, Dec 22 2018