A010555 a(n) = 1 if n is the product of an even number of distinct primes, otherwise a(n) = -1.

1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1

Offset

1,1

Comments

The old definition was mobius(mobius(n)). The reason for this sequence was that in some ancient version of Maple the command "with(numtheory): A010555 := n->mobius(mobius(n));" worked. But it no longer works, so the definition has been changed.

Links

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

Formula

a(n) = (-1)^(1-A353629(n)). - Antti Karttunen, Jan 17 2025

Prog

(PARI) A010555(n) = if(1==moebius(n), 1, -1); \\ Antti Karttunen, Jan 17 2025

Crossrefs

Cf. A008683, A030229 (positions of positive terms), A353629 (their characteristic function).

Sequence in context: A119664 A257075 A330034 * A108784 A127252 A244513

Adjacent sequences: A010552 A010553 A010554 * A010556 A010557 A010558

Keyword

sign,easy,changed

Author

N. J. A. Sloane

Extensions

Definition changed by N. J. A. Sloane, Jan 15 2019

Status

approved