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A359469
a(n) = A353459(n) mod 2.
3
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1
OFFSET
1
FORMULA
For all n >= 1, a(n) = a(A003961(n)) = a(A348717(n)).
PROG
(PARI)
A353457(n) = { my(f=factor(n)); prod(i=1, #f~, if(!(primepi(f[i, 1])%2), 1, if(f[i, 2]==1, -1, 0))); };
A353458(n) = { my(f=factor(n)); prod(i=1, #f~, if(primepi(f[i, 1])%2, 1, if(f[i, 2]==1, -1, 0))); };
A353459(n) = (A353457(n)+A353458(n));
A359469(n) = (A353459(n)%2);
(Python)
from functools import reduce
from operator import iand
from sympy import factorint, primepi
def A359469(n):
f = [(primepi(p)&1, int(e==1)) for p, e in factorint(n).items()]
return reduce(iand, (e for p, e in f if not p), 1)^reduce(iand, (e for p, e in f if p), 1) # Chai Wah Wu, Jan 06 2023
CROSSREFS
Characteristic function of A359470.
Differs from A359466 and A359467 for the first time at n=100, as here a(100) = 1.
Sequence in context: A345952 A359466 A359467 * A107078 A341613 A163533
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 04 2023
STATUS
approved