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)^3 for n > 1. Indeed, by A291539 and A291540, PrimePi(n^3) > PrimePi(n) * PrimePi(n^2) > PrimePi(n)^3 for n > 7.
For prime(n)^3 - prime(n^3), see A262199.
For PrimePi(n^2) - PrimePi(n)^2, see A291440.
FORMULA
EXAMPLE
a(3) = PrimePi(3^3) - PrimePi(3)^3 = 9 - 2^3 = 1.
MATHEMATICA
Table[ PrimePi[n^3] - PrimePi[n]^3, {n, 60}]
PROG
(PARI) a(n) = primepi(n^3) - primepi(n)^3; \\ Michel Marcus, Sep 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, following a suggestion from Altug Alkan, Aug 25 2017
STATUS
approved