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A365647
Dirichlet convolution of Dedekind psi function with reduced totient function.
2
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
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
KEYWORD
nonn
AUTHOR
Torlach Rush, Sep 14 2023
STATUS
approved