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A356163
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a(n) = 1 if sum of prime factors of n (taken with multiplicity) is even, otherwise 0.
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10
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1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1
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OFFSET
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1
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LINKS
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FORMULA
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For x, y >= 1, a(x*y) >= a(x) * a(y).
a(x*y) = 1 - a(x) - a(y) + 2*a(x)*a(y). - Robert Israel, Nov 03 2022
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MAPLE
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f:= proc(n) local t; 1-add(t[1]*t[2], t = ifactors(n)[2]) mod 2 end proc:
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MATHEMATICA
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{1}~Join~Array[Boole@ EvenQ[Total[Times @@@ FactorInteger[#]]] &, 119, 2] (* Michael De Vlieger, Nov 02 2022 *)
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PROG
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(PARI)
(Python)
from functools import reduce
from operator import ixor, and_
from itertools import starmap
from sympy import factorint
def A356163(n): return (reduce(ixor, starmap(and_, factorint(n).items()), 0)&1)^1 # Chai Wah Wu, Dec 21 2022
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CROSSREFS
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Characteristic function of A036349, whose complement A335657 gives the positions of 0's.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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