

A237710


Least prime p < n with pi(np) a square, or 0 if such a prime p does not exist.


5



0, 0, 2, 2, 3, 5, 5, 7, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 2, 2, 2, 2, 2, 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13
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OFFSET

1,3


COMMENTS

According to the conjecture in A237706, a(n) should be positive for all n > 2.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
Z.W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014


EXAMPLE

a(5) = 3 since pi(53) = 1^2, but pi(52) = 2 is not a square.


MATHEMATICA

SQ[n_]:=IntegerQ[Sqrt[n]]
q[n_]:=SQ[PrimePi[n]]
Do[Do[If[q[nPrime[k]], Print[n, " ", Prime[k]]; Goto[aa]], {k, 1, PrimePi[n1]}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 100}]


CROSSREFS

Cf. A000040, A000290, A000720, A237706.
Sequence in context: A316185 A131429 A105605 * A090473 A113636 A262463
Adjacent sequences: A237707 A237708 A237709 * A237711 A237712 A237713


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 12 2014


STATUS

approved



