\\ invsigma comes from Max Alekseyev's following page: https://home.gwu.edu/~maxal/gpscripts/invphi.gp

upperbounds() = {my(d = divisors(63540409508528099686942221), res = vector(1000), printnxt = 100); 
	for(i = 1, #d, 
		if(i > printnxt, 
			print1(i", "); printnxt += 100;
		);
		inv = invsigma(d[i]); 
		if(#inv > #res, 
			res = concat(res, #inv - #res);
		);
		if(#inv > 0, 
			if(res[#inv] == 0, 
				res[#inv] = d[i]; 
				print(); print(); 
				print(#inv" "d[i]); 
				print(); print()
			)
		)
	); res
}