login
Square root of the smallest square referenced in A038109 (Divisible exactly by the square of a prime).
3

%I #17 Nov 14 2020 05:26:54

%S 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 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 2,3,17,2,7,2,3,2,3,2,2,5,2,3,13,2,3,2

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

%C 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 Robert Israel, <a href="/A284017/b284017.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = sqrt(A284018(n)). - _Amiram Eldar_, Nov 14 2020

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

%p N:= 1000: # to use the members of A038109 <= N

%p P:= select(isprime, [$1..floor(sqrt(N))]):

%p S:= {}:

%p for p in P do

%p Ks:= select(t -> t mod p <> 0, {$1..floor(N/p^2)});

%p R:= map(`*`,Ks,p^2) minus S;

%p for r in R do B[r]:= p od:

%p S:= S union R;

%p od:

%p A038109:= sort(convert(S,list)):

%p seq(B[A038109[i]], i=1..nops(A038109)); # _Robert Israel_, Mar 28 2017

%t 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 Cf. A038109, A284018.

%K nonn

%O 1,1

%A _Robert Price_, Mar 18 2017

%E Corrected by _Robert Israel_, Mar 28 2017