A359549 a(n) = 1 if n is either an odd squarefree number squared or twice such a number, otherwise 0.

1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 1, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

Multiplicative with a(2^e) = 1 if e=1, a(2^e) = 0 if e > 1, and for odd primes p, a(p^e) = 1 if e=2, a(p^e) = 0 if e=1 or e>2.

a(n) = abs(A359548(n)) = A359548(n) mod 2.

a(n) = A046692(n) mod 2 = A327276(n) mod 2 = A327278(n) mod 2.

Mathematica

a[n_] := If[(e = IntegerExponent[n, 2]) < 2 && SquareFreeQ[Sqrt[n/2^e]], 1, 0] ; Array[a, 100] (* Amiram Eldar, Jan 07 2023 *)

Prog

(PARI) A359549(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], (1==f[k, 2]), (2==f[k, 2]))); };
(Python)
from sympy import factorint
def A359549(n): return int((m:=(~n & n-1).bit_length())<2 and all(e==2 for e in factorint(n>>m).values())) # Chai Wah Wu, Jan 11 2023

Crossrefs

Characteristic function of A359580.

Absolute values of A359548, also their parity.

Parity of A046692, A327276, A327278.

Cf. A227291, A359818 (Dirichlet inverse).

Sequence in context: A167700 A010057 A359548 * A359773 A359774 A204220

Adjacent sequences: A359546 A359547 A359548 * A359550 A359551 A359552

Keyword

nonn,mult

Author

Antti Karttunen, Jan 06 2023

Status

approved