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

Author

Torlach Rush, Sep 14 2023

Keywords

• nonn

Crossrefs

Cf. A000040, A000203, A002322, A365647.

Programs

Mathematica

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

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))

Formula

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

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