cp's OEIS Frontend

A245777 Denominator of (n / tau(n) - sigma(n) / n).

%I A245777 #21 Sep 08 2022 08:46:09
%S A245777 1,2,6,12,10,2,14,8,9,10,22,3,26,14,20,80,34,6,38,30,84,22,46,2,75,26,
%T A245777 108,3,58,20,62,96,44,34,140,36,74,38,156,4,82,28,86,33,30,46,94,60,
%U A245777 147,150,68,78,106,36,220,7,228,58,118,5,122,62,126,448,260
%N A245777 Denominator of (n / tau(n) - sigma(n) / n).
%C A245777 Denominator of (n / A000005(n) - A000203(n) / n).
%C A245777 See A245776 - numerator of (n / tau(n) - sigma(n) / n).
%C A245777 If n is an odd prime, a(n) = 2*n. - _Robert Israel_, Aug 01 2014
%C A245777 First deviation from A245785 (denominator of (n/tau(n) +  sigma(n)/n)) is at a(300); a(300) = 75, A245785(300) = 25. Sequence of numbers n such that A245785(n) is not equal to a(n): 300, 768, 1452, 1764, 2100, 3468, 3900, 5376, 5700, 6084, 6348, 9075, 9300, ... See (Magma) [n: n in [1..10000] | (Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n))) - (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) ne 0] - _Jaroslav Krizek_, Aug 15 2014
%H A245777 Michael De Vlieger, <a href="/A245777/b245777.txt">Table of n, a(n) for n = 1..10000</a>
%F A245777 A245776(n) / a(n) < 1 for numbers n in A245779.
%F A245777 A245776(n) / a(n) = integer for numbers n in A245778.
%F A245777 a(n) = 1 for numbers n in A245778.
%e A245777 For n = 9; a(9) = denominator(9/tau(9) - sigma(9)/9) = denominator(9/3 - 13/9) = denominator(14/9) = 9.
%t A245777 Table[Denominator[n/DivisorSigma[0, n] - DivisorSigma[1, n]/n], {n, 70}] (* _Alonso del Arte_, Aug 15 2014 *)
%o A245777 (Magma) [Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n)): n in [1..100]]
%o A245777 (PARI) vector(150, n, denominator(n/numdiv(n) - sigma(n)/n)) \\ _Derek Orr_, Aug 01 2014
%Y A245777 Cf. A000005, A000203, A245776, A245778, A245779, A245782.
%K A245777 nonn,frac
%O A245777 1,2
%A A245777 _Jaroslav Krizek_, Aug 01 2014