A positive integer m belongs to this sequence iff A243700(1) + A243700(2) + ... + A243700(m) is not 0 modulo m.

Based on an analysis by John Pezzullo of the b-file of 30542 terms it appears that a(n) is growing like cn, where c is approximately 3 - see the link. - Alexander R. Povolotsky, Jun 19 2014