OFFSET
1,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = 1 - A001222(n) mod 2.
a(n) = A007421(n) - 1.
a(n) = 1 - A066829(n).
Dirichlet g.f.: (zeta(s)^2 + zeta(2*s))/(2*zeta(s)). - Enrique Pérez Herrero, Jul 06 2012
a(n) = (A008836(n) + 1)/2. - Enrique Pérez Herrero, Jul 07 2012
a(n) = A001222(2n) mod 2. - Wesley Ivan Hurt, Jun 22 2013
G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} x^(n^2)/(1 - x^n). - Ilya Gutkovskiy, Apr 25 2017
From Antti Karttunen, Dec 01 2022: (Start)
For x, y >= 1, a(x*y) = 1 - abs(a(x)-a(y)).
a(n) >= A356170(n).
(End)
MAPLE
A065043 := proc(n)
if type(numtheory[bigomega](n), 'even') then
1;
else
0;
end if;
end proc: # R. J. Mathar, Jun 26 2013
MATHEMATICA
Table[(LiouvilleLambda[n]+1)/2, {n, 1, 20}] (* Enrique Pérez Herrero, Jul 07 2012 *)
PROG
(PARI) { for (n=1, 1000, a=1 - bigomega(n)%2; write("b065043.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 04 2009
(PARI) A065043(n) = (1 - (bigomega(n)%2)); \\ Antti Karttunen, Apr 19 2022
(Python)
from operator import ixor
from functools import reduce
from sympy import factorint
def A065043(n): return (reduce(ixor, factorint(n).values(), 0)&1)^1 # Chai Wah Wu, Jan 01 2023
CROSSREFS
Characteristic function of A028260 (positions of 1's). Cf. also A026424 (positions of 0's) and A320655.
One less than A007421.
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 05 2001
EXTENSIONS
Corrected by Charles R Greathouse IV, Sep 02 2009
STATUS
approved