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 A347871 a(n) = (n+A003415(sigma(n))) mod 2, where A003415 gives the arithmetic derivative of its argument. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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 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:  A347857 A347858 A347870 * A347872 A347873 A347874 KEYWORD nonn AUTHOR Antti Karttunen, Sep 17 2021 STATUS approved

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Last modified January 20 07:44 EST 2022. Contains 350467 sequences. (Running on oeis4.)