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

%I A284018 #18 Nov 14 2020 05:24:56
%S A284018 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,
%T A284018 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,
%U A284018 4,9,4,25,4,9,4,9,289,4,49,4,9,4,9,4,4,25,4
%N A284018 The smallest square referenced in A038109 (Divisible exactly by the square of a prime).
%C A284018 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
%H A284018 Robert Israel, <a href="/A284018/b284018.txt">Table of n, a(n) for n = 1..10000</a>
%F A284018 a(n) = A284017(n)^2. - _Amiram Eldar_, Nov 14 2020
%e A284018 A038109(3)=12, 12 = 2*2*3, so 12 is divisible by the square of 2 which is 4.
%p A284018 N:= 1000: # to use the members of A038109 <= N
%p A284018 P:= select(isprime, [$1..floor(sqrt(N))]):
%p A284018 S:= {}:
%p A284018 for p in P do
%p A284018   Ks:= select(t -> t mod p <> 0, {$1..floor(N/p^2)});
%p A284018   R:= map(`*`, Ks, p^2) minus S;
%p A284018   for r in R do B[r]:= p^2 od:
%p A284018   S:= S union R;
%p A284018 od:
%p A284018 A038109:= sort(convert(S, list)): seq(B[A038109[i]], i=1..nops(A038109));# _Robert Israel_, Mar 28 2017
%t A284018 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 *)
%Y A284018 Cf. A038109, A284017, A013929, A283919.
%K A284018 nonn
%O A284018 1,1
%A A284018 _Robert Price_, Mar 18 2017
%E A284018 Corrected by _Robert Israel_, Mar 28 2017