A067931 Numbers k that divide the alternating sum sigma(1) - sigma(2) + sigma(3) - sigma(4) + ... + ((-1)^(k+1))*sigma(k).

1, 2, 11, 19, 36, 45, 152, 377, 418, 3794, 4423, 14495, 31148, 42224, 49279, 120447, 1018376, 2605261, 17484247, 368070997, 850833878, 1121254607, 3440701629, 7863041200

Offset: 1

Author

Joseph L. Pe, Feb 22 2002

Keywords

• nonn
• more

Comments

No further term below 10^7.

a(25) > 5*10^10. - Donovan Johnson, Jul 26 2011

Examples

			sigma(1) - sigma(2) = -2, which is divisible by 2, so 2 is a term of the sequence.
		

Crossrefs

Cf. A000203, A068762.

Programs

Mathematica

s = 0; Do[s = s + (-1)^(i + 1) * DivisorSigma[1, i]; If[Mod[s, i] == 0, Print[i]], {i, 1, 10^5}]

PARI

{a067931(m)=local(s,n); s=0; for(n=1,m, if(n%2==0,s=s-sigma(n),s=s+sigma(n)); if(s%n==0,print1(n,",")))}

Extensions

Edited and extended by Klaus Brockhaus, Feb 28 2002

a(19)-a(24) from Donovan Johnson, Jul 26 2011