A340769 The third-smallest divisor of n-th square number, n>1.

4, 9, 4, 25, 3, 49, 4, 9, 4, 121, 3, 169, 4, 5, 4, 289, 3, 361, 4, 7, 4, 529, 3, 25, 4, 9, 4, 841, 3, 961, 4, 9, 4, 7, 3, 1369, 4, 9, 4, 1681, 3, 1849, 4, 5, 4, 2209, 3, 49, 4, 9, 4, 2809, 3, 11, 4, 9, 4, 3481, 3, 3721, 4, 7, 4, 13, 3, 4489, 4, 9, 4, 5041, 3

Offset: 2

Author

Charles Kusniec, Jan 20 2021

Keywords

• nonn

Comments

The terms are either primes or squares of primes.

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A020639, A000290, A000040, A001248, A000430.

Programs

Maple

f:= proc(n) local F,t;
  F:= sort(ifactors(n)[2],(a,b) -> a[1]= 2 and F[2,1] < F[1,1]^2 then F[2,1] else F[1,1]^2 fi
end proc:
map(f, [$2..100]); # Robert Israel, Oct 09 2024

Mathematica

a[n_] := Divisors[n^2][[3]]; Array[a, 100, 2] (* Amiram Eldar, Jan 20 2021 *)

PARI

a(n) = divisors(n^2)[3]; \\ Michel Marcus, Jan 20 2021