s = 0
unseen = 1
seen(v) = bit test(s, v)
see(v) = s = bit or(s, 2^v); while (seen(unseen), unseen++)

rad(n) = vecprod(factor(n)[,1]~)

rr = vector(3, k, 1)	\\ radical of 3 previous terms

other() = {
	my (forbidden = gcd(rr),
	    mandatory = rr[#rr] / gcd(rr[#rr], forbidden));
	forstep (v=mandatory*ceil(unseen/mandatory), oo, mandatory,
		if (!seen(v) && gcd(v, forbidden)==1,
			see(v);
			rr = concat(rr[2..#rr], rad(v));
			return (v);
		);
	);
}

for (n=1, 10 000, print (n " " other()))

quit