A284017 Square root of the smallest square referenced in A038109 (Divisible exactly by the square of a prime).

2, 3, 2, 3, 2, 5, 2, 2, 2, 3, 7, 5, 2, 2, 3, 2, 3, 5, 2, 2, 3, 2, 7, 3, 2, 2, 2, 3, 11, 2, 3, 2, 2, 3, 7, 2, 5, 3, 2, 2, 13, 3, 2, 5, 2, 2, 2, 3, 5, 2, 3, 2, 2, 3, 2, 3, 2, 11, 2, 7, 2, 2, 3, 2, 5, 2, 3, 2, 3, 17, 2, 7, 2, 3, 2, 3, 2, 2, 5, 2, 3, 13, 2, 3, 2

Offset

1,1

Comments

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

Links

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

Formula

a(n) = sqrt(A284018(n)). - Amiram Eldar, Nov 14 2020

Example

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

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 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 &] (* Amiram Eldar, Nov 14 2020 *)

Crossrefs

Cf. A038109, A284018.

Sequence in context: A303779 A087242 A123556 * A236454 A053669 A342309

Adjacent sequences: A284014 A284015 A284016 * A284018 A284019 A284020

Keyword

nonn

Author

Robert Price, Mar 18 2017

Extensions

Corrected by Robert Israel, Mar 28 2017

Status

approved