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Numerator of (n/tau(n) - sigma(n)/n).
5

%I #19 Sep 08 2022 08:46:09

%S 0,-1,1,-5,13,-1,33,1,14,7,97,-1,141,25,43,101,253,5,321,37,313,85,

%T 481,1,532,127,569,8,781,27,897,323,299,235,1033,53,1293,301,1297,11,

%U 1597,83,1761,179,173,457,2113,133,2230,971,771,529,2701,163,2737,34,2929,751,3361,11,3597,865,1115

%N Numerator of (n/tau(n) - sigma(n)/n).

%C Numerator of (n/A000005(n) - A000203(n)/n).

%C See A245777 - denominator of (n/tau(n) - sigma(n)/n).

%H Michael De Vlieger, <a href="/A245776/b245776.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n)/A245777(n) < 1 for numbers n in A245779.

%F a(n)/A245777(n) is an integer for numbers n in A245778.

%F a(n) = 1 for n = 3, 8 and 24.

%F a(n) < 0 for n = 2, 4, 6 and 12.

%e For n = 9; a(9) = numerator(9/tau(9) - sigma(9)/9) = numerator(9/3 - 13/9) = numerator(14/9) = 14.

%t a245776[n_Integer] :=

%t Map[Numerator[#/DivisorSigma[0, #] - DivisorSigma[1, #]/#] &,

%t Range[n]]; a245776[63] (* _Michael De Vlieger_, Aug 07 2014 *)

%o (Magma) [Numerator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n)): n in [1..1000]]

%o (PARI) vector(150, n, numerator(n/numdiv(n) - sigma(n)/n)) \\ _Derek Orr_, Aug 01 2014

%Y Cf. A000005, A000203, A245777, A245778, A245779, A245782.

%K sign,frac

%O 1,4

%A _Jaroslav Krizek_, Aug 01 2014