A369601 Dirichlet convolution of totient function with reduced totient function.

1, 2, 4, 5, 8, 8, 12, 10, 16, 16, 20, 18, 24, 24, 28, 22, 32, 32, 36, 36, 42, 40, 44, 36, 56, 48, 60, 54, 56, 56, 60, 48, 70, 64, 84, 70, 72, 72, 84, 72, 80, 84, 84, 90, 108, 88, 92, 78, 120, 112, 112, 108, 104, 120, 140, 108

Offset

1,2

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = Sum_{d|n} A000010(d) * A002322(n/d).

Example

a(4) = phi(1)*lambda(4) + phi(2)*lambda(2) + phi(4)*lambda(1) = 5, where lambda is Carmichael's reduced totient function.

Mathematica

a[n_]:=Sum[EulerPhi[d]CarmichaelLambda[n/d], {d, Divisors[n]}]; Array[a, 56] (* Stefano Spezia, Jan 27 2024 *)

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*lcm(znstar(n/d)[2]))

Crossrefs

Cf. A000010, A002322.

Sequence in context: A036694 A085624 A331376 * A345426 A061884 A286002

Adjacent sequences: A369598 A369599 A369600 * A369602 A369603 A369604

Keyword

nonn,easy

Author

Miles Englezou, Jan 26 2024

Status

approved