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

1, -2, 2, -5, 1, -11, -3, -18, -5, -23, -11, -39, -25, -49, -25, -56, -38, -77, -57, -99, -67, -103, -79, -139, -108, -150, -110, -166, -136, -208, -176, -239, -191, -245, -197, -288, -250, -310, -254, -344, -302, -398, -354, -438, -360, -432, -384, -508, -451, -544, -472, -570, -516, -636, -564, -684, -604

Offset: 1

Author

Klaus Brockhaus, Feb 28 2002

Keywords

• easy
• sign

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A067931.

Programs

Mathematica

Accumulate[Times@@@Partition[Riffle[DivisorSigma[1,Range[60]],{1,-1},{2,-1,2}],2]] (* Harvey P. Dale, Dec 12 2014 *)
Accumulate[Table[-(-1)^k*DivisorSigma[1, k], {k, 1, 60}]] (* Vaclav Kotesovec, Aug 07 2022 *)

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,","))

Formula

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

a(n) ~ -Pi^2 * n^2 / 48. - Vaclav Kotesovec, Aug 07 2022