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%I #6 Dec 10 2024 09:59:35
%S 1,1,3,2,5,1,7,1,9,1,11,2,13,1,15,4,17,1,19,2,21,1,23,3,25,1,27,2,29,
%T 1,31,1,33,1,35,2,37,1,39,1,41,1,43,2,45,1,47,4,49,1,51,2,53,1,55,1,
%U 57,1,59,2,61,1,63,2,65,1,67,2,69,1,71,3,73,1,75,2
%N a(n) = gcd(n, A007814(n)).
%H Amiram Eldar, <a href="/A378888/b378888.txt">Table of n, a(n) for n = 1..10000</a>
%F a(2*n-1) = 2*n-1.
%F a(2*n) = A378887(n).
%F Sum_{k=1..n} a(k) ~ n^2/4 + c*n/2, where c = 1.62390224555724623579... is the asymptotic mean of A378887 (see the Formula section of A378887).
%t a[n_] := GCD[n, IntegerExponent[n, 2]]; Array[a, 100]
%o (PARI) a(n) = gcd(n, valuation(n, 2));
%Y Cf. A007814, A378887 (even bisection).
%K nonn,easy,new
%O 1,3
%A _Amiram Eldar_, Dec 10 2024