

A243903


Numbers n such that (number of primes <= n) is greater than or equal to (number of semiprimes <= n).


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32, 33
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OFFSET

1,2


COMMENTS

Conjecture: there are no additional terms.
We know from the asymptotic formulas (see Landau) that the sequence is finite. See also the graph of A243906.  N. J. A. Sloane, Jun 14 2014


REFERENCES

E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 1, Teubner, Leipzig, 1909; third edition : Chelsea, New York (1974).


LINKS



MATHEMATICA

With[{nn=5000}, Flatten[Position[Thread[{Accumulate[Table[ If[ PrimeOmega[n] == 2, 1, 0], {n, nn}]], PrimePi[Range[nn]]}], _?(Last[#]>=First[#]&), {1}, Heads> False]]]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



