A054586 - OEIS

%I #14 Aug 12 2023 04:37:01

%S 1,-1,-3,-5,-1,-9,-11,3,-15,-17,5,-21,-3,-1,-27,-29,9,15,-35,11,-39,

%T -41,3,-45,-5,15,-51,27,17,-57,-59,5,33,-65,21,-69,-71,3,45,-77,-1,

%U -81,45,27,-87,55,29,51,-95,9,-99,-101,-15,-105,-107,35,-111,63,11,75,-9

%N a(n) = Sum_{d|2n+1} phi(d)*mu(d).

%D David M. Burton, Elementary Number Theory, Allyn and Bacon Inc., Boston, MA, 1976, p. 152.

%F a(n) = A276833(2*n+1). - _Amiram Eldar_, Aug 12 2023

%t a[n_] := DivisorSum[2*n+1, MoebiusMu[#]*EulerPhi[#]&]; Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Dec 03 2015 *)

%t f[p_, e_] := 2-p; a[n_] := Times @@ f @@@ FactorInteger[2*n+1]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 12 2023 *)

%o (PARI) j=[]; for(n=0,200,j=concat(j,sumdiv(2*n+1,d,moebius(d)*eulerphi(d)))); j

%Y Cf. A276833.

%K sign

%O 0,3

%A _N. J. A. Sloane_, Apr 12 2000

%E Wrong formula deleted by _Amiram Eldar_, Aug 12 2023