A354981 a(n) = 1 if n = 2 * p^k, with p an odd prime and k >= 1, otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = [n == 2 (mod 4)] * A069513(n/2), where [ ] is the Iverson bracket.

For n > 4, a(n) = A211487(n) - A174275(n).

Mathematica

a[n_] := If[IntegerExponent[n, 2] == 1 && PrimePowerQ[n/2], 1, 0]; Array[a, 100] ( * Amiram Eldar, Jun 15 2022 *)
Module[{nn=150, c}, c=Union[Flatten[Table[2 p^k, {p, Prime[Range[2, 35]]}, {k, 5}]]]; Table[If[ MemberQ[ c, k], 1, 0], {k, nn}]] (* Harvey P. Dale, Sep 18 2023 *)

Prog

(PARI) A354981(n) = (2==(n%4) && isprimepower(n/2));

Crossrefs

Characteristic function of A278568 \ {2}.

Cf. A069513, A174275, A211487, A354108.

Sequence in context: A361463 A104853 A358775 * A231600 A347579 A280710

Adjacent sequences: A354978 A354979 A354980 * A354982 A354983 A354984

Keyword

nonn

Author

Antti Karttunen, Jun 15 2022

Status

approved