A329071 - OEIS

%I #12 Nov 05 2019 10:40:39

%S 0,2,3,3,5,2,7,2,5,1,11,5,13,4,7,5,17,1,19,7,6,4,23,1,6,5,7,6,29,4,31,

%T 1,13,6,11,7,37,8,7,4,41,3,43,13,6,8,47,7,13,3,19,7,53,4,7,3,11,9,59,

%U 6,61,16,11,7,17,5,67,19,20,4,71,4,73,17,11,11

%N a(n) = phi(A275314(n)) - mu(A275314(n)), where A275314(n) is Euler's gradus function.

%F a(n) = phi(A275314(n)) - mu(A275314(n)) where phi is Euler's totient function (A000010) and mu is the Mobius function (A008683).

%t gradus[n_] := 1 + Plus @@ ((First[#] - 1) * Last[#] & /@ FactorInteger[n]); a[n_] := EulerPhi[(g = gradus[n])] - MoebiusMu[g]; Array[a, 76] (* _Amiram Eldar_, Nov 03 2019 *)

%o (PARI) g(n) = my(f = factor(n)); sum(k=1, #f~, (f[k, 1]-1)*f[k, 2])+ 1; \\ A275314

%o a(n) = my(gn = g(n)); eulerphi(gn) - moebius(gn); \\ _Michel Marcus_, Nov 04 2019

%Y Cf. A000010, A008683, A275314.

%K nonn

%O 1,2

%A _Daniel Hoyt_, Nov 03 2019