prob127(N)=
{
	\\ this is very inefficient.  could be partly because the "factor" bit in pari/gp
	\\ may write files the factors to disk in the event of large factors
	\\ so a memory mapped or solid state disk could make this a faster.
	\\ the mattranspose function may be unnecessary as well.
	\\ answer = 18407904
	s = 15938116;
	for(c=114245,N,
		for (b=1,c-1,
			if (gcd(b,c) == 1,
				a = c - b;
				if (a < b,
					if (gcd(a,c) == 1,
						if (gcd(b,c) == 1,
							f = mattranspose(vecextract(factor(a * b * c),1)); \\ the unique factors, in a column
							m = 1;
							z = Vec(f);
							for (i=1,length(f), m *= (z[i][1]));
							if (m < c,
								s += c;
								print1(c);
								print1(": ");
								print(s);
							);
						);
					);
				);
			);
		);
	);
}