A365648 Dirichlet convolution of sigma with reduced totient function.

1, 4, 6, 12, 10, 24, 14, 30, 27, 40, 22, 70, 26, 56, 56, 70, 34, 108, 38, 116, 78, 88, 46, 172, 75, 104, 108, 162, 58, 224, 62, 158, 122, 136, 128, 310, 74, 152, 144, 284, 82, 312, 86, 254, 242, 184, 94, 396, 147, 300, 188, 300, 106, 432, 200, 396, 210, 232, 118

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = Sum{d|n} A000203(d) * A002322(n/d).

a(p) = A365647(p) where p is a term of A000040.

Mathematica

Table[DirichletConvolve[DivisorSigma[1, k], CarmichaelLambda[k], k, n], {n, 1, 100}] (* Amiram Eldar, Sep 15 2023 *)

Prog

(Python)
from sympy import divisors, reduced_totient, divisor_sigma
def a(n): return sum(divisor_sigma(d, 1) * reduced_totient(n//d) for d in divisors(n))

Crossrefs

Cf. A000040, A000203, A002322, A365647.

Sequence in context: A110758 A189765 A074162 * A038040 A143356 A058270

Adjacent sequences: A365645 A365646 A365647 * A365649 A365650 A365651

Keyword

nonn

Author

Torlach Rush, Sep 14 2023

Status

approved