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A347871
a(n) = (n+A003415(sigma(n))) mod 2, where A003415 gives the arithmetic derivative of its argument.
7
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.
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. also A343223.
Sequence in context: A131078 A302203 A130657 * A185916 A084846 A285498
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 17 2021
STATUS
approved