A374466 a(n) = 1 if n is the product of an odd number of primes and the total number of 1-bits in the exponents of its prime factorization is odd, 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, 1

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) = A066829(n) * (1-A359464(n)) = A000035(A001222(n)) * A000035(A064547(n)).

Prog

(PARI)
A064547(n) = { my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); };
A066829(n) = (bigomega(n)%2);
A374466(n) = ((A064547(n)%2) * A066829(n));

Crossrefs

Characteristic function of A374467.

Cf. A000035, A001222, A064547, A359464.

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

Differs from A374130 first at n=128, where a(128) = 1, while A374130(128) = 0.

Sequence in context: A358751 A252233 A374130 * A283991 A380455 A353499

Adjacent sequences: A374463 A374464 A374465 * A374467 A374468 A374469

Keyword

nonn

Author

Antti Karttunen, Jul 14 2024

Status

approved