prime exp(v) = {
	my (x = []);
	forprime (p = 2, oo,
		if (v==1,
				return (x),
				x = concat(x, valuation(v, p));
				v /= p^x[#x];
		);
	);
}

mix(a, b) = vector(max(#a, #b), n, if (n <= #a, a[n], 0) + if (n <= #b, b[n], 0))

apex(i, j) = {
	my (v = []);
	for (k = i, j,
		v = mix(v, binomial(j-i, k-i) * f[k]);
	);
	return (v);
}

{
	for (n = 1, #f = vector(100),
		for (v = 2, oo,
			f[n] = prime exp(v);
			r = vector(n, i, apex(i, n));

			ok = 1;

			for (i = 1, n-1,
				for (j = i, n-1,
					m = apex(i, j);
					for (k = 1, n,
						if (m==r[k],
							ok = 0;
							break (3);
						);
					);
				);
			);

			if (ok,
				print (n " " v);
				break;
			);
		);
	);
}

quit