
COMMENTS

This sequence is a subsequence of the sequence {b(n)} defined as follows:
"Odious numbers which can be written as a product of evil numbers." It differs from A230213 only at the 56th term (b_{56} = a(3) = 575.
An algorithm for calculation of {b(n)} is the following: Consider an odious number n. Let d_1 be the smallest evil divisor of n (if n does not have an evil divisor, then n is not in {b(n)}). If n/d_1 is either evil or odious but is already in {b(n)}, then n is in this sequence. If n/d_1 is odious and not in the sequence, then we consider the following evil divisor d_2 > d_1 (if d_2 does not exist, then n is not in {b(n)}). If n/d_2 is either evil or odious but already in this sequence, then n is in {b(n)}, etc. Formally, by a continuation of {b(n)} sufficiently far, we can calculate terms a(k), k=2,3,4,... A direct calculation, say, a(4) is connected with the finding of 4 evil primes p,q,r,s with the smallest possible product, such that all 11 numbers p*q, p*r, p*s, q*r, q*s, r*s, p*q*r, p*q*s, p*r*s, q*r*s, p*q*r*s* are odious. In this case we find p=5, q=5, r=23, s=89, such that a(4) = 5*5*23*89 = 51175.
