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A067931
Numbers k that divide the alternating sum sigma(1) - sigma(2) + sigma(3) - sigma(4) + ... + ((-1)^(k+1))*sigma(k).
2
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
1,2
COMMENTS
No further term below 10^7.
a(25) > 5*10^10. - Donovan Johnson, Jul 26 2011
EXAMPLE
sigma(1) - sigma(2) = -2, which is divisible by 2, so 2 is a term of the sequence.
MATHEMATICA
s = 0; Do[s = s + (-1)^(i + 1) * DivisorSigma[1, i]; If[Mod[s, i] == 0, Print[i]], {i, 1, 10^5}]
PROG
(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, ", ")))}
CROSSREFS
Sequence in context: A152312 A154765 A163997 * A186267 A067660 A235472
KEYWORD
nonn,more
AUTHOR
Joseph L. Pe, Feb 22 2002
EXTENSIONS
Edited and extended by Klaus Brockhaus, Feb 28 2002
a(19)-a(24) from Donovan Johnson, Jul 26 2011
STATUS
approved