A347132 a(n) = Sum_{d|n} A001615(n/d) * A003415(d), where A003415 is the arithmetic derivative and A001615 is Dedekind psi function.

0, 1, 1, 7, 1, 12, 1, 30, 10, 16, 1, 65, 1, 20, 18, 104, 1, 83, 1, 93, 22, 28, 1, 254, 16, 32, 63, 121, 1, 167, 1, 320, 30, 40, 26, 391, 1, 44, 34, 374, 1, 215, 1, 177, 143, 52, 1, 840, 22, 165, 42, 205, 1, 450, 34, 494, 46, 64, 1, 827, 1, 68, 183, 912, 38, 311, 1, 261, 54, 295, 1, 1430, 1, 80, 197, 289, 38, 359

Offset

1,4

Comments

Dirichlet convolution of Dedekind psi function (A001615) with the arithmetic derivative (A003415).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = Sum_{d|n} A001615(n/d) * A003415(d).

Mathematica

Table[DivisorSum[n, DirichletConvolve[j, MoebiusMu[j]^2, j, n/#]*If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &], {n, 78}] (* Michael De Vlieger, Oct 19 2021, after Jan Mangaldan at A001615 *)

Prog

(PARI)
A001615(n) = if(1==n, n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A347132(n) = sumdiv(n, d, A001615(n/d)*A003415(d));

Crossrefs

Cf. A001615, A003415.

Cf. also A305809, A322577, A347131, A347133, A347135.

Sequence in context: A343227 A339965 A364094 * A349173 A347965 A013600

Adjacent sequences: A347129 A347130 A347131 * A347133 A347134 A347135

Keyword

nonn

Author

Antti Karttunen, Aug 23 2021

Status

approved