

A094189


Number of primes between n^2n and n^2 (inclusive).


7



0, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 2, 2, 3, 4, 4, 3, 4, 3, 3, 4, 5, 4, 3, 4, 5, 4, 4, 5, 4, 4, 5, 5, 2, 6, 6, 5, 4, 6, 4, 5, 7, 7, 3, 7, 8, 4, 5, 10, 7, 5, 6, 5, 5, 10, 7, 8, 8, 6, 10, 7, 5, 5, 8, 7, 7, 5, 10, 7, 8, 10, 7, 7, 10, 10, 9, 12, 7, 11, 10, 10, 9, 7, 13, 11, 10, 10, 11, 10, 11, 10, 11
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OFFSET

1,2


COMMENTS

Conjecture: for n>11, a(n)>1.
Oppermann conjectured in 1882 that a(n)>0 for n>1.  T. D. Noe, Sep 16 2008


REFERENCES

Paulo Ribenboim, The New Book of Prime Number Records, 3rd ed., 1995, Springer, p. 248.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
Wikipedia, Oppermann's conjecture


MATHEMATICA

Table[PrimePi[n^2]PrimePi[n^2n1], {n, 100}] (* Harvey P. Dale, Jul 24 2015 *)


PROG

(PARI) a(n) = sum(k=n^2n, n^2, isprime(k))
(PARI) a(n)=my(s); forprime(p=n^2n, n^2, s++); s \\ Charles R Greathouse IV, Jan 18 2016
(Haskell)
a094189 n = sum $ map a010051' [n*(n1) .. n^2]
 Reinhard Zumkeller, Jun 07 2015


CROSSREFS

Cf. A014085, A089610, A108309, A010051.
Sequence in context: A008967 A211355 A211353 * A122771 A217710 A112190
Adjacent sequences: A094186 A094187 A094188 * A094190 A094191 A094192


KEYWORD

easy,nonn


AUTHOR

Jason Earls, May 25 2004


STATUS

approved



