OFFSET
1,2
COMMENTS
All terms are positive except a(1) = 0, by the PNT with error term for large n and computation for smaller n. In particular, PrimePi(n^3) > PrimePi(n) * PrimePi(n)^2 for n > 1.
For PrimePi(n) * PrimePi(n^2) - PrimePi(n)^3, see A291540.
For PrimePi(n^3) - PrimePi(n)^3, see A291538.
For prime(n) * prime(n^2) - prime(n^3), see A291541.
FORMULA
EXAMPLE
a(2) = PrimePi(2^3) - PrimePi(2) * PrimePi(2^2) = 4 - 1 * 2 = 2.
MATHEMATICA
Table[ PrimePi[n^3] - PrimePi[n]*PrimePi[n^2], {n, 60}]
PROG
(PARI) a(n) = primepi(n^3) - primepi(n) * primepi(n^2); \\ Michel Marcus, Sep 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Aug 25 2017
STATUS
approved