OFFSET
0
COMMENTS
Characteristic function of A056911.
Dirichlet inverse of A166698. - Antti Karttunen, Dec 19 2022
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
Jon Maiga, Computer-generated formulas for A323239, Sequence Machine.
FORMULA
For n >= 1:
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/Pi^2 (A185199). - Amiram Eldar, Jul 24 2022
From Antti Karttunen, Dec 19 2022: (Start)
Multiplicative with a(p^e) = 1 if p > 2 and e = 1, otherwise 0.
(End)
Dirichlet g.f.: zeta(s)/(zeta(2*s)*(1+1/2^s)). - Amiram Eldar, Dec 27 2022
a(n) = Sum_{d|n} A359548(d). [From Sequence Machine] - Antti Karttunen, Nov 22 2023
MAPLE
f:= n -> charfcn[{true}](n::odd and numtheory:-issqrfree(n)):
map(f, [$0..200]); # Robert Israel, Jan 14 2019
MATHEMATICA
Table[If[OddQ[n]&&SquareFreeQ[n], 1, 0], {n, 0, 120}] (* Harvey P. Dale, Feb 02 2021 *)
PROG
(PARI) A323239(n) = ((n%2) && issquarefree(n));
(PARI) A323239(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 1]%2)*(1==f[k, 2])); }; \\ Antti Karttunen, Dec 19 2022
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Jan 12 2019
EXTENSIONS
Keyword:mult added by Antti Karttunen, Dec 19 2022
STATUS
approved