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

%I A284017 #17 Nov 14 2020 05:26:54
%S A284017 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,
%T A284017 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,
%U A284017 2,3,17,2,7,2,3,2,3,2,2,5,2,3,13,2,3,2
%N A284017 Square root of the smallest square referenced in A038109 (Divisible exactly by the square of a prime).
%C A284017 a(n) is the least prime p whose exponent in the prime factorization of A038109(n) is exactly 2. - _Robert Israel_, Mar 28 2017
%H A284017 Robert Israel, <a href="/A284017/b284017.txt">Table of n, a(n) for n = 1..10000</a>
%F A284017 a(n) = sqrt(A284018(n)). - _Amiram Eldar_, Nov 14 2020
%e A284017 A038109(3)=12, 12 = 2*2*3, so 12 is divisible by the square of 2.
%p A284017 N:= 1000: # to use the members of A038109 <= N
%p A284017 P:= select(isprime, [$1..floor(sqrt(N))]):
%p A284017 S:= {}:
%p A284017 for p in P do
%p A284017   Ks:= select(t -> t mod p <> 0, {$1..floor(N/p^2)});
%p A284017   R:= map(`*`,Ks,p^2) minus S;
%p A284017   for r in R do B[r]:= p od:
%p A284017   S:= S union R;
%p A284017 od:
%p A284017 A038109:= sort(convert(S,list)):
%p A284017 seq(B[A038109[i]], i=1..nops(A038109)); # _Robert Israel_, Mar 28 2017
%t A284017 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 *)
%Y A284017 Cf. A038109, A284018.
%K A284017 nonn
%O A284017 1,1
%A A284017 _Robert Price_, Mar 18 2017
%E A284017 Corrected by _Robert Israel_, Mar 28 2017