A331314 Dirichlet convolution of the identity function with the reduced totient function.

1, 3, 5, 8, 9, 15, 13, 18, 21, 27, 21, 38, 25, 39, 41, 40, 33, 63, 37, 68, 59, 63, 45, 84, 65, 75, 81, 98, 57, 123, 61, 88, 95, 99, 105, 156, 73, 111, 113, 150, 81, 177, 85, 158, 165, 135, 93, 184, 133, 195

Offset

1,2

Comments

This sequence differs from A018804 when A002322 differs from A000010.

Links

Table of n, a(n) for n=1..50.

Formula

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

Mathematica

a[n_] := DivisorSum[n, # * CarmichaelLambda[n/#] &]; Array[a, 50] (* Amiram Eldar, Jan 13 2020 *)

Prog

(PARI) a(n) = sumdiv(n, d, d * lcm(znstar(n/d)[2])); \\ Daniel Suteu, Jan 13 2020
(Magma) [1] cat [&+[d*CarmichaelLambda(n div d):d in Set(Divisors(n)) diff {n}]+n:n in [2..60]]; // Marius A. Burtea, Jan 14 2020

Crossrefs

Cf. A000010 (phi), A002322 (psi), A018804 (Pillai's arithmetical function).

Sequence in context: A138808 A185456 A308405 * A018804 A032682 A022769

Adjacent sequences: A331311 A331312 A331313 * A331315 A331316 A331317

Keyword

nonn

Author

Torlach Rush, Jan 13 2020

Status

approved