A374130 a(n) = 1 if bitwise-XOR of the exponents of primes in the prime factorization of n is equal to 1, otherwise 0.

0, 1, 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, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = [A268387(n) = 1], where [ ] is the Iverson bracket.

For k in A268390, a(A059897(n,k)) = a(n).

Mathematica

A374130[n_] := If[n == 1, 0, Boole[BitXor @@ FactorInteger[n][[All, 2]] == 1]];
Array[A374130, 100] (* Paolo Xausa, Jul 16 2024 *)

Prog

(PARI)
A268387(n) = { my(f=factor(n), b=0); for(k=1, #f~, b = bitxor(b, f[k, 2]); ); b; }; \\ From A268387
A374130(n) = (1==A268387(n));

Crossrefs

Characteristic function of A374595.

Cf. A059897, A268387, A268390.

Differs from A252233 first at n=72, where a(72) = 1, while A252233(72) = 0.

Differs from A374466 first at n=128, where a(128) = 0, while A374466(128) = 1.

Sequence in context: A010051 A358751 A252233 * A374466 A283991 A353499

Adjacent sequences: A374127 A374128 A374129 * A374131 A374132 A374133

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Jul 14 2024

Status

approved