A353788 - OEIS

%I #18 May 13 2022 18:24:58

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

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

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

%N a(n) = 1 if the number of divisors of n is either 2 or 4, otherwise 0.

%H Antti Karttunen, <a href="/A353788/b353788.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F a(n) = 1 if A010052(n) == 0 [n is not a square] and A000005(n) <= 4, otherwise 0.

%F a(n) = [A084115(n) == 1], where [ ] is the Iverson bracket.

%F a(n) = 1 if A101296(n) is either 2, 4 or 5, otherwise 0.

%F For n > 1, a(n) = A353799(n) - A302048(n).

%t a[n_] := If[MemberQ[{2, 4}, DivisorSigma[0, n]], 1, 0]; Array[a, 120] (* _Amiram Eldar_, May 13 2022 *)

%o (PARI) A353788(n) = (!issquare(n) && (numdiv(n)<=4));

%o (PARI) A353788(n) = (isprime(n) || (4==numdiv(n)));

%Y Characteristic function of A084116.

%Y Cf. A000005, A000290, A010051, A010052, A101296, A302048, A353799.

%Y Cf. also A353787.

%K nonn

%O 1

%A _Antti Karttunen_, May 13 2022