upto(n) = {
	ulim = n; qchecks = 0; 
	res = List(); 
	process([1, 1, 1]); 
	listsort(res, 1); print(qchecks);
	res
}

process(v) = {my(p, e, np);
	qchecks++; 
	if(ispowerful(sigma(v[1])), print1(v[1]", "); listput(res, v[1])); 
	np = nextprime(v[2] + 1); 
	for(e = 2, logint(ulim \ v[1], 2),
		 
		forprime(p = np, sqrtnint(ulim \ v[1], e),  
			
			process([v[1]*p^e, p])
		)
	)	
}


\\ispowerful(n) = my(f = factor(n)); vecmin(f[, 2]) > 1