A354108 a(n) = 1 if n is neither an odd prime power nor twice an odd prime power, otherwise 0.

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

Offset

1

Comments

See comments in A354109 for a proof of the equivalence of the formulas.

Links

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

Index entries for characteristic functions

Formula

For n > 4, a(n) = 1 - A211487(n).

a(n) = 1 if A354107(n) is equal to A353768(n), otherwise 0.

a(n) = 1 iff A010873(abs(A354101(n))) is 0.

a(n) = [A000010(n) == A354102(n) (mod 4)], where [ ] is the Iverson bracket.

a(n) >= A354188(n).

Mathematica

a[n_] := If[! (OddQ[n] && PrimePowerQ[n]) && ! (OddQ[n/2] && PrimePowerQ[n/2]), 1, 0]; Array[a, 100] (* Amiram Eldar, May 20 2022 *)

Prog

(PARI) A354108(n) = ((n && !bitand(n, n-1)) || !isprimepower(n/(2-(n%2))));
(PARI) A354108(n) = (A353768(n) == A353768(A267099(n)));

Crossrefs

Characteristic function of A354109.

Cf. A000010, A010873, A211487, A353768, A267099, A354101, A354102, A354107, A354188.

Sequence in context: A353518 A353687 A354918 * A181101 A321512 A297054

Adjacent sequences: A354105 A354106 A354107 * A354109 A354110 A354111

Keyword

nonn

Author

Antti Karttunen, May 18 2022

Status

approved