\\ da(n) = a(n) - a(n - 1)
da(n) = {my(d = divisors(n), res = if(issquare(n), numdiv(sqrtint(n)), 0)); 
for(i = 1, #d \ 2, 
	res+=(numdiv(d[i]) + numdiv(n / d[i]) - numdiv(gcd(d[i], n / d[i]))) << 1
); res
}

first(n) = {my(res = vector(n)); res[1] = 1;  
for(i = 2, n, 
	res[i] = res[i - 1] + da(i)
); res
}