A354819 a(n) = 1 if n is a nonprime squarefree number, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A008966(n) * (1-A010051(n)).

For all n >= 1, a(n) = a(A046523(n)).

For all n > 1, a(n) <= A354353(n).

Mathematica

a[n_] := If[!PrimeQ[n] && SquareFreeQ[n], 1, 0]; Array[a, 100] (* Amiram Eldar, Jun 11 2022 *)

Prog

(PARI) A354819(n) = ((1!=bigomega(n))&&issquarefree(n));
(Python)
from sympy import factorint
def A354819(n): return int(n==1 or (len(f:=factorint(n))>1 and max(f.values())==1)) # Chai Wah Wu, Nov 08 2025

Crossrefs

Characteristic function of A000469.

Cf. A008966, A010051, A046523, A322075, A354353, A354870 (inverse Möbius transform).

Sequence in context: A339661 A374471 A320656 * A322075 A369255 A378215

Adjacent sequences: A354816 A354817 A354818 * A354820 A354821 A354822

Keyword

nonn

Author

Antti Karttunen, Jun 10 2022

Status

approved