[seqfan] A166460, A068499

[Don Reble]

Seqfans:

> %C A166460 Is this the complement of A068499? [R. J. Mathar]

    Yes, except that they both have "1".

    If N is odd and at least 5, then N+1 = 2*a, 2 < a < N,
                 N! = N*...*a*...*2*1
        A068499: N+1 divides N!            : absent
        A166460: N-1 is even and composite : present
    If N is even and N+1 is prime,
        A068499: N+1 does not divide N!    : present
        A166460: N+1 is prime              : absent
    If N is even and N+1 = p^2 is the square of a (odd) prime,
                 then N+1 >= 3p, N > 2p.
        A068499: N! = N*...*2p*...*p*...*1;
                 N+1 divides N!            : absent
        A166460: N+1 is composite          : present
    If N is even and N+1 is composite but not the square of a prime,
                 then there are two distinct factors a*b = N+1:
                 3 <= a < b = (N+1)/a < N.
        A068499: N! = N*...*b*...*a*...*1:
                 N+1 divides N!            : absent
        A166460: N+1 is composite          : present

    Those cover all Ns except 0,1,3.

-- 
Don Reble  djr at nk.ca