A329071 a(n) = phi(A275314(n)) - mu(A275314(n)), where A275314(n) is Euler's gradus function.

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

Offset: 1

Author

Daniel Hoyt, Nov 03 2019

Keywords

• nonn

Crossrefs

Cf. A000010, A008683, A275314.

Programs

Mathematica

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 *)

PARI

g(n) = my(f = factor(n)); sum(k=1, #f~, (f[k, 1]-1)*f[k, 2])+ 1; \\ A275314
a(n) = my(gn = g(n)); eulerphi(gn) - moebius(gn); \\ Michel Marcus, Nov 04 2019

Formula

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