A355444 - OEIS

%I #12 Jul 07 2022 19:52:21

%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N a(n) = 1 if n is of the form p^2 * q where p and q are primes with p < q < p^2, otherwise 0.

%H Antti Karttunen, <a href="/A355444/b355444.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A353472(n) * A355454(n).

%F a(n) = A353474(n) - A355443(n).

%t a[n_] := If[(f = FactorInteger[n])[[;; , 2]] == {2, 1} && f[[1, 1]]^2 > f[[2, 1]], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 07 2022 *)

%o (PARI) A355444(n) = ((numdiv(n) == (3+bigomega(n))) && issquare(divisors(n)[4]));

%Y Characteristic function of A355446.

%Y Cf. A353472, A353474, A355443, A355454.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 02 2022