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

1,2

Links

Table of n, a(n) for n=1..76.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000010, A008683, A275314.

Sequence in context: A205130 A324799 A069461 * A232932 A252502 A063256

Adjacent sequences: A329068 A329069 A329070 * A329072 A329073 A329074

Keyword

nonn

Author

Daniel Hoyt, Nov 03 2019

Status

approved