A347871 a(n) = (n+A003415(sigma(n))) mod 2, where A003415 gives the arithmetic derivative of its argument.

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

Offset

1

Comments

a(n) = 0 if n and A342925(n) have the same parity, otherwise 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) = A342926(n) mod 2.

a(n) = A000035(n) XOR A347870(n) = 1 - [A347870(n) = A000035(n)], where XOR is the bitwise-XOR and [ ] is the Iverson bracket.

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); a[n_] := Mod[n + ad[DivisorSigma[1, n]], 2]; Array[a, 105] (* Amiram Eldar, Sep 18 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A347871(n) = ((n+A003415(sigma(n)))%2);

Crossrefs

Sequence A342926 read modulo 2.

Characteristic function of A347873, whose complement A347872 gives the positions of zeros.

Cf. A000035, A000203, A003415, A342925, A347870, A347883.

Cf. also A343223.

Sequence in context: A131078 A302203 A130657 * A185916 A084846 A285498

Adjacent sequences: A347868 A347869 A347870 * A347872 A347873 A347874

Keyword

nonn

Author

Antti Karttunen, Sep 17 2021

Status

approved