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A379007 a(n) = (n^2) XOR ((n^2)-1).

%I A379007 #28 Jan 13 2025 01:26:05
%S A379007 1,7,1,31,1,7,1,127,1,7,1,31,1,7,1,511,1,7,1,31,1,7,1,127,1,7,1,31,1,
%T A379007 7,1,2047,1,7,1,31,1,7,1,127,1,7,1,31,1,7,1,511,1,7,1,31,1,7,1,127,1,
%U A379007 7,1,31,1,7,1,8191,1,7,1,31,1,7,1,127,1,7,1,31,1,7,1,511,1,7,1,31,1,7,1,127,1,7,1,31,1,7,1,2047
%N A379007 a(n) = (n^2) XOR ((n^2)-1).
%H A379007 Antti Karttunen, <a href="/A379007/b379007.txt">Table of n, a(n) for n = 1..20000</a>
%H A379007 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%F A379007 Multiplicative with a(p^e) = 2^(1+2*e)-1 if p = 2; 1 if p > 2.
%F A379007 a(n) = A038712(A000290(n)).
%F A379007 a(n) = A000225(A037227(n)) = (2^(1+2*A007814(n))) - 1.
%F A379007 Dirichlet g.f.: zeta(s) * (2^s + 2)/(2^s - 4). - _Amiram Eldar_, Jan 12 2025
%t A379007 Map[BitXor[#, # - 1] &, Range[100]^2] (* _Paolo Xausa_, Dec 18 2024 *)
%o A379007 (PARI) A379007(n) = bitxor(n^2, ((n^2)-1));
%o A379007 (Python)
%o A379007 def A379007(n): return (m:=n**2)^m-1 # _Chai Wah Wu_, Dec 17 2024
%Y A379007 Cf. A000225, A000290, A003987, A007814, A037227, A038712.
%Y A379007 Cf. also A283750.
%K A379007 nonn,mult
%O A379007 1,2
%A A379007 _Antti Karttunen_, Dec 16 2024