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A068762 Alternating sum sigma(1)-sigma(2)+sigma(3)-sigma(4)+...+((-1)^(n+1))*sigma(n). 5

%I

%S 1,-2,2,-5,1,-11,-3,-18,-5,-23,-11,-39,-25,-49,-25,-56,-38,-77,-57,

%T -99,-67,-103,-79,-139,-108,-150,-110,-166,-136,-208,-176,-239,-191,

%U -245,-197,-288,-250,-310,-254,-344,-302,-398,-354,-438,-360,-432,-384,-508,-451,-544,-472,-570,-516,-636,-564,-684,-604

%N Alternating sum sigma(1)-sigma(2)+sigma(3)-sigma(4)+...+((-1)^(n+1))*sigma(n).

%H Harvey P. Dale, <a href="/A068762/b068762.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = sum((-1)^(k+1)*sigma(k), k=1..n)

%e a(3) = sigma(1) - sigma(2) + sigma(3) = 1 - 3 + 4 = 2.

%t Accumulate[Times@@@Partition[Riffle[DivisorSigma[1,Range[60]],{1,-1},{2,-1,2}],2]] (* _Harvey P. Dale_, Dec 12 2014 *)

%o (PARI) a068762(m)=local(s,n); s=0; for(n=1,m, if(n%2==0,s=s-sigma(n),s=s+sigma(n)); print1(s,","))

%Y Cf. A000203, A067931.

%K easy,sign

%O 1,2

%A _Klaus Brockhaus_, Feb 28 2002

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Last modified January 22 08:31 EST 2021. Contains 340360 sequences. (Running on oeis4.)