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A176095 a(n) = n - phi(2*n), where phi() is the Euler totient A000010().

%I A176095 #26 Dec 21 2023 01:15:34
%S A176095 0,0,1,0,1,2,1,0,3,2,1,4,1,2,7,0,1,6,1,4,9,2,1,8,5,2,9,4,1,14,1,0,13,
%T A176095 2,11,12,1,2,15,8,1,18,1,4,21,2,1,16,7,10,19,4,1,18,15,8,21,2,1,28,1,
%U A176095 2,27,0,17,26,1,4,25,22,1,24,1,2,35,4,17,30,1,16,27,2,1,36,21,2,31,8,1,42,19
%N A176095 a(n) = n - phi(2*n), where phi() is the Euler totient A000010().
%D A176095 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
%D A176095 Tom M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 24.
%H A176095 Antti Karttunen, <a href="/A176095/b176095.txt">Table of n, a(n) for n = 1..16384</a>
%H A176095 Antti Karttunen, <a href="/A176095/a176095.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A176095 a(n) = n - A062570(n).
%F A176095 a(2^k) = 0, k >= 0. - _Michel Lagneau_, Dec 17 2010
%F A176095 a(A000040(k)) = 1, k >= 2. - _Michel Lagneau_, Dec 17 2010, corrected by _Antti Karttunen_, May 19 2021
%F A176095 a(2^m*A000040(k)) = 2^m, m >= 1, k >= 2. - _Michel Lagneau_, Dec 17 2010
%F A176095 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 - 8/Pi^2 = 0.1894305... . - _Amiram Eldar_, Dec 21 2023
%e A176095 a(1) = 1 - phi(2) = 0;
%e A176095 a(2) = 2 - phi(2*2) = 2 - 2 = 0;
%e A176095 a(3) = 3 - phi(2*3) = 3 - 2 = 1;
%e A176095 If n = (2^m)*p, with m = 3 and p = 7, then n = 2^3 * 7 = 56, and a(56) = 2^3 = 8.
%p A176095 A176095 := proc(n)
%p A176095     n-numtheory[phi](2*n) ;
%p A176095 end proc:
%p A176095 seq(A176095(n),n=1..60) ;
%t A176095 Table[n-EulerPhi[2n],{n,0,100}] (* _Harvey P. Dale_, Jul 24 2011 *)
%o A176095 (PARI) A176095(n) = (n-eulerphi(n+n)); \\ _Antti Karttunen_, May 19 2021
%Y A176095 Cf. A000010, A000040, A051953, A062570.
%K A176095 nonn,easy
%O A176095 1,6
%A A176095 _Michel Lagneau_, Apr 08 2010
%E A176095 Offset corrected; entry corrected and edited by _Michel Lagneau_, Apr 25 2010