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A080545 Characteristic function of {1} union {odd primes}: 1 if n is 1 or an odd prime, else 0.

%I A080545 #20 Aug 08 2025 11:47:55
%S A080545 1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,
%T A080545 0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,
%U A080545 0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0
%N A080545 Characteristic function of {1} union {odd primes}: 1 if n is 1 or an odd prime, else 0.
%H A080545 Antti Karttunen, <a href="/A080545/b080545.txt">Table of n, a(n) for n = 1..1001</a>
%H A080545 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A080545 a(n) = (delta(Omega(n), 0) + delta(Omega(n), 1)) * d_0(n), where delta is the Kronecker delta function, Omega is the number of prime factors function (counted with multiplicity), and d_0(n) is the least significant digit of n in binary. - _Alonso del Arte_, Nov 19 2013
%e A080545 a(2) = 0 because 2 is prime but even.
%e A080545 a(3) = 1 because 3 is prime and odd. Likewise for a(5) and a(7).
%e A080545 a(4) = 0 because 4 is neither prime nor odd. Likewise for a(6) and a(8).
%e A080545 a(9) = 0 because 9 is odd but composite.
%t A080545 Table[Boole[PrimeOmega[n] < 2 && OddQ[n]], {n, 100}] (* _Alonso del Arte_, Nov 19 2013 *)
%Y A080545 Cf. A010051, A080355, A080567, A171387.
%Y A080545 Differs from A080339 only at a(2).
%K A080545 nonn,easy
%O A080545 1,1
%A A080545 _N. J. A. Sloane_, Mar 21 2003
%E A080545 Added missing a(2) - _Walter Roscello_, Nov 19 2013