OFFSET
1,2
COMMENTS
10^19 < a(9) <= 725298909352131113041. Terms a(3) through a(8) all have the prime signature p^4*q^2*r^2. Any x such that sigma(x) = -1 (mod 30) must have at least eight prime factors. However, for all n, there are solutions with fewer than three distinct prime factors. More generally, for any k > 1, let p be a prime of the form mk+1; then sigma(p^(k-2)) = -1 (mod k). For a(9), 725298909352131113041 is the least solution with eight prime factors. I have not been able to rule out a smaller solution with more prime factors. - David Wasserman, Dec 14 2007
EXAMPLE
Smallest numbers x are collected, whose sigma[x] has 2k+1,6k+5,30k+29,210k+209 etc.. form; i.e. for which 1+sigma[x] is divisible by the n-th primorial number
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Aug 19 2004
EXTENSIONS
More terms from David Wasserman, Dec 14 2007
STATUS
approved