A354035 a(n) = 1 if n is odd and sigma(n^2) == 3 (mod 4), otherwise 0.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = A000035(n) * A000035(A083025(n)).

a(n) = A000035(n) * [A010873(A065764(n)) == 3], where [ ] is the Iverson bracket.

a(n) = A000035(n) - A354036(n).

Mathematica

a[n_] := If[OddQ[n] && Mod[DivisorSigma[1, n^2], 4] == 3, 1, 0]; Array[a, 100] (* Amiram Eldar, May 16 2022 *)

Prog

(PARI) A354035(n) = ((n%2)&&3==(sigma(n*n)%4));

Crossrefs

Characteristic function of A324909.

Cf. A000035, A000203, A010873, A065764, A083025, A354036.

Sequence in context: A358678 A359150 A354031 * A025457 A350289 A219463

Adjacent sequences: A354032 A354033 A354034 * A354036 A354037 A354038

Keyword

nonn

Author

Antti Karttunen, May 16 2022

Status

approved