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

%I A068762 #9 Aug 07 2022 09:01:01
%S A068762 1,-2,2,-5,1,-11,-3,-18,-5,-23,-11,-39,-25,-49,-25,-56,-38,-77,-57,
%T A068762 -99,-67,-103,-79,-139,-108,-150,-110,-166,-136,-208,-176,-239,-191,
%U A068762 -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 A068762 Alternating sum sigma(1)-sigma(2)+sigma(3)-sigma(4)+...+((-1)^(n+1))*sigma(n).
%H A068762 Harvey P. Dale, <a href="/A068762/b068762.txt">Table of n, a(n) for n = 1..1000</a>
%F A068762 a(n) = sum((-1)^(k+1)*sigma(k), k=1..n)
%F A068762 a(n) ~ -Pi^2 * n^2 / 48. - _Vaclav Kotesovec_, Aug 07 2022
%e A068762 a(3) = sigma(1) - sigma(2) + sigma(3) = 1 - 3 + 4 = 2.
%t A068762 Accumulate[Times@@@Partition[Riffle[DivisorSigma[1,Range[60]],{1,-1},{2,-1,2}],2]] (* _Harvey P. Dale_, Dec 12 2014 *)
%t A068762 Accumulate[Table[-(-1)^k*DivisorSigma[1, k], {k, 1, 60}]] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o A068762 (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 A068762 Cf. A000203, A067931.
%K A068762 easy,sign
%O A068762 1,2
%A A068762 _Klaus Brockhaus_, Feb 28 2002