A329308 - OEIS

%I #27 Sep 08 2022 08:46:24

%S 0,0,0,0,0,1,1,0,0,1,2,1,0,2,1,1,0,2,2,1,2,1,3,0,1,1,3,1,2,3,1,2,0,3,

%T 2,1,1,4,4,0,2,2,4,1,1,1,3,2,1,3,3,3,3,2,4,2,2,1,4,1,3,2,2,0,2,5,5,2,

%U 3,2,3,1,1,3,5,0,5,3,3,2,1,3,6,2,2,5,3,3,1,2,3,4,3,3,4,1,1,4,2

%N a(n) is the number of k with 1 < k < sqrt(n) such that n mod k^2 is prime.

%H Robert Israel, <a href="/A329308/b329308.txt">Table of n, a(n) for n = 1..10000</a>

%e a(11) = 2 because 11 == 3 (mod 2^2) and 11 == 2 (mod 3^2), and 2 and 3 are prime.

%p f:= proc(n) local k; nops(select(isprime, [seq(n mod k^2, k=2..floor(sqrt(n)))])) end proc:

%p map(f, [$1..100]);

%t a[n_] := Select[Range[2, Sqrt[n] // Floor], PrimeQ[Mod[n, #^2]]&] // Length;

%t Array[a, 100] (* _Jean-François Alcover_, Jul 17 2020 *)

%o (Magma) a:=[]; for n in [1..100] do Append(~a,#[k:k in [2..Floor(Sqrt(n))]| IsPrime(n mod k^2) ]); end for; a; // _Marius A. Burtea_, Nov 11 2019

%o (PARI) a(n) = sum(j=2, sqrtint(n), isprime(n % j^2)); \\ _Michel Marcus_, Nov 11 2019

%Y Cf. A329203, A329309.

%K nonn

%O 1,11

%A _J. M. Bergot_ and _Robert Israel_, Nov 09 2019