A283670 The single square referenced in A190641.

4, 4, 9, 4, 4, 9, 4, 4, 25, 9, 4, 4, 4, 4, 9, 4, 49, 25, 4, 9, 4, 4, 9, 4, 4, 25, 4, 4, 9, 4, 4, 9, 4, 4, 49, 9, 4, 4, 4, 9, 4, 121, 4, 25, 9, 4, 4, 9, 4, 4, 49, 4, 25, 4, 9, 4, 4, 9, 4, 4, 169, 9, 4, 25, 4, 4, 4, 9, 4, 9, 4, 9, 4, 4, 4, 4, 4, 4, 9, 4, 4

Offset: 1

Author

Robert Price, Mar 13 2017

Keywords

• nonn

Examples

			A190641(4) = 12, 12 = 2*2*3, so 12 has only one square factor, namely 4.
		

Links

• Robert Price, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A190641, A249739, A283671.

Programs

Mathematica

f[n_] := Module[{f = FactorInteger[n], ind}, ind = Position[f[[;;, 2]], ?(# > 1 &)]; If[Length[ind] == 1, f[[ind[[1, 1]],1]]^2, Nothing]]; Array[f, 300] (* _Amiram Eldar, Jul 28 2024 *)

PARI

lista(kmax) = for(k = 1, kmax, my(f = factor(k)); if(#select(x -> (x>1), f[,2]) == 1, for(i = 1, #f~, if(f[i,2] > 1, print1(f[i,1]^2, ", "); break)))); \\ Amiram Eldar, Jul 28 2024

Formula

a(n) = A283671(n)^2 = A249739(A190641(n))^2. - Amiram Eldar, Jul 28 2024