A284018 The smallest square referenced in A038109 (Divisible exactly by the square of a prime).

4, 9, 4, 9, 4, 25, 4, 4, 4, 9, 49, 25, 4, 4, 9, 4, 9, 25, 4, 4, 9, 4, 49, 9, 4, 4, 4, 9, 121, 4, 9, 4, 4, 9, 49, 4, 25, 9, 4, 4, 169, 9, 4, 25, 4, 4, 4, 9, 25, 4, 9, 4, 4, 9, 4, 9, 4, 121, 4, 49, 4, 4, 9, 4, 25, 4, 9, 4, 9, 289, 4, 49, 4, 9, 4, 9, 4, 4, 25, 4

Offset: 1

Author

Robert Price, Mar 18 2017

Keywords

• nonn

Comments

a(n) = p^2 where p is the least prime whose exponent in the prime factorization of A038109(n) is exactly 2. - Robert Israel, Mar 28 2017

Examples

			A038109(3)=12, 12 = 2*2*3, so 12 is divisible by the square of 2 which is 4.
		

Links

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

Crossrefs

Cf. A038109, A284017, A013929, A283919.

Programs

Maple

N:= 1000: # to use the members of A038109 <= N
P:= select(isprime, [$1..floor(sqrt(N))]):
S:= {}:
for p in P do
  Ks:= select(t -> t mod p <> 0, {$1..floor(N/p^2)});
  R:= map(`*`, Ks, p^2) minus S;
  for r in R do B[r]:= p^2 od:
  S:= S union R;
od:
A038109:= sort(convert(S, list)): seq(B[A038109[i]], i=1..nops(A038109));# Robert Israel, Mar 28 2017

Mathematica

s[n_] := If[(pos = Position[(f = FactorInteger[n])[[;; , 2]], 2]) == {}, 1, f[[pos[[1, 1]], 1]]]; Select[Array[s, 300], # > 1 &]^2 (* Amiram Eldar, Nov 14 2020 *)

Formula

a(n) = A284017(n)^2. - Amiram Eldar, Nov 14 2020

Extensions

Corrected by Robert Israel, Mar 28 2017