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A355935 Dirichlet inverse of A091862, characteristic function of numbers for which A267116(n) = bigomega(n), where A267116 is the bitwise-OR of the exponents of primes in the prime factorization of n.

%I A355935 #10 Jul 22 2022 10:38:15
%S A355935 1,-1,-1,0,-1,2,-1,0,0,2,-1,-2,-1,2,2,0,-1,-2,-1,-2,2,2,-1,2,0,2,0,-2,
%T A355935 -1,-6,-1,0,2,2,2,6,-1,2,2,2,-1,-6,-1,-2,-2,2,-1,-2,0,-2,2,-2,-1,2,2,
%U A355935 2,2,2,-1,10,-1,2,-2,0,2,-6,-1,-2,2,-6,-1,-8,-1,2,-2,-2,2,-6,-1,-2,0,2,-1,10,2,2,2,2,-1,10,2,-2,2,2,2,2,-1,-2,-2,6,-1,-6,-1,2,-6
%N A355935 Dirichlet inverse of A091862, characteristic function of numbers for which A267116(n) = bigomega(n), where A267116 is the bitwise-OR of the exponents of primes in the prime factorization of n.
%H A355935 Antti Karttunen, <a href="/A355935/b355935.txt">Table of n, a(n) for n = 1..100000</a>
%H A355935 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A355935 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A091862(n/d) * a(d).
%t A355935 s[n_] := If[n == 1 || PrimeOmega[n] == BitOr @@ FactorInteger[n][[;; , 2]], 1, 0]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, s[n/#]*a[#] &, # < n &]; Array[a, 100] (* _Amiram Eldar_, Jul 21 2022 *)
%o A355935 (PARI)
%o A355935 A267116(n) = if(1==n, 0, fold(bitor, factor(n)[, 2]));
%o A355935 A091862(n) = (bigomega(n)==A267116(n));
%o A355935 memoA355935 = Map();
%o A355935 A355935(n) = if(1==n,1,my(v); if(mapisdefined(memoA355935,n,&v), v, v = -sumdiv(n,d,if(d<n,A091862(n/d)*A355935(d),0)); mapput(memoA355935,n,v); (v)));
%Y A355935 Cf. A091862, A267116, A268375.
%K A355935 sign
%O A355935 1,6
%A A355935 _Antti Karttunen_, Jul 21 2022