Add to n its second smallest non-divider. Loop

[N. J. A. Sloane]

I have some trouble to find an index entry for this :
Is the following sequence (or some equivalent variant) present :

A??? Number of 3-factor Carmichael numbers having prime(n) as least factor

(It is known that there is only a finite number of C's with k factors,
once k-2 factors are given,
but I don't know if it is straightforward to compute.)

Also the following sequence (which IS straightforward to compute)
seems not yet on OEIS, but I (resp. my program, i.e. we both) may be
wrong :

A??? Number of 3-factor Carmichael numbers having prime(n) as largest factor
0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 0,
0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
2, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0,
0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1

I'd appreciate any information from someone more familiar with related
entries existing in OEIS.

Maximilian