OFFSET
1,1
COMMENTS
Conjecture: The sequence has infinitely many terms.
See also A262700 for a related conjecture.
REFERENCES
Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..1000 (n = 1..200 from Zhi-Wei Sun)
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
EXAMPLE
a(2) = 8 since pi(8^2)*pi(2^2) = 18*2 = 6^2.
a(3) = 10 since pi(10^2)*pi(3^2) = 25*4 = 10^2.
MATHEMATICA
f[n_]:=PrimePi[n^2]
SQ[n_]:=IntegerQ[Sqrt[n]]
n=0; Do[Do[If[SQ[f[x]*f[y]], n=n+1; Print[n, " ", y]; Goto[aa]], {x, 2, y-1}]; Label[aa]; Continue, {y, 1, 870}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Sep 27 2015
STATUS
approved