A365647 Dirichlet convolution of Dedekind psi function with reduced totient function.

1, 4, 6, 11, 10, 24, 14, 26, 26, 40, 22, 64, 26, 56, 56, 58, 34, 104, 38, 106, 78, 88, 46, 148, 74, 104, 102, 148, 58, 224, 62, 128, 122, 136, 128, 272, 74, 152, 144, 244, 82, 312, 86, 232, 232, 184, 94, 326, 146, 296, 188, 274, 106, 408, 200, 340, 210, 232, 118

Offset

1,2

Links

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

Formula

a(n) = Sum{d|n} A001615(d) * A002322(n/d).

a(p) = A365648(p) where p is a term of A000040.

Mathematica

psi[n_Integer] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Table[DirichletConvolve[psi[k], CarmichaelLambda[k], k, n], {n, 1, 100}] (* Amiram Eldar, Sep 15 2023 *)

Prog

(Python)
from sympy import divisors, primefactors, prod, reduced_totient
def psi(n):
    return n*prod(p+1 for p in primefactors(n))//prod(primefactors(n))
def a(n): return sum(psi(d) * reduced_totient(n//d) for d in divisors(n))

Crossrefs

Cf. A000040, A001615, A002322, A365648.

Sequence in context: A012903 A273103 A187215 * A322577 A013018 A031271

Adjacent sequences: A365644 A365645 A365646 * A365648 A365649 A365650

Keyword

nonn

Author

Torlach Rush, Sep 14 2023

Status

approved