A354036 a(n) = 1 if n is odd and sigma(n^2) == 1 (mod 4), otherwise 0.

1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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) * [A010873(A065764(n)) == 1], where [ ] is the Iverson bracket.

a(n) = A000035(n) - A354035(n).

Mathematica

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

Prog

(PARI) A354036(n) = ((n%2)&&1==(sigma(n*n)%4));

Crossrefs

Characteristic function of A354039.

Cf. A000035, A000203, A010873, A065764, A083025, A354035.

Sequence in context: A285142 A267525 A014429 * A284948 A011637 A016229

Adjacent sequences: A354033 A354034 A354035 * A354037 A354038 A354039

Keyword

nonn

Author

Antti Karttunen, May 16 2022

Status

approved