A275258 Toth's partial sum over the number of divisors of the greatest unitary divisor.

1, 3, 4, 6, 6, 11, 8, 11, 11, 16, 12, 21, 14, 21, 23, 20, 18, 29, 20, 32, 30, 31, 24, 39, 27, 36, 30, 42, 30, 57, 32, 37, 45, 46, 47, 56, 38, 51, 52, 59, 42, 77, 44, 62, 63, 61, 48, 71, 51, 69, 67, 72, 54, 77, 70, 78, 74, 76, 60, 113, 62, 81, 83

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

László Tóth, On the Bi-Unitary Analogues of Euler's Arithmetical Function and the Gcd-Sum Function, JIS 12 (2009), Article 09.5.2, function S**(n).

Formula

a(n) = Sum_{k=1..n} A000005( A165430(n,k) ).

Sum_{k=1..n} a(k) = c * n^2 / 2 + O(n * log(n)^2), where c = A065486. - Amiram Eldar, Dec 22 2023

Maple

A275258 := proc(n)
    local a, d ;
    a := 0 ;
    for  d in A077610(n) do
        a := a+A005361(d)*A275257(n/d, d) ;
    end do:
    a ;
end proc:
seq(A275258(n), n=1..80) ;

Mathematica

beta[n_] := Times @@ Transpose[FactorInteger[n]][[2]]; phi[x_, n_] := Sum[Boole[ GCD[k, n] == 1 ], {k, 1, x}]; a[n_] := DivisorSum[n, beta[#] * phi[n/#, #] &, GCD[#, n/#] == 1 &]; Array[a, 100] (* Amiram Eldar, Sep 22 2019 *)

Crossrefs

Cf. A000005, A065486, A165430.

Sequence in context: A053158 A206924 A185443 * A230593 A304411 A360522

Adjacent sequences: A275255 A275256 A275257 * A275259 A275260 A275261

Keyword

nonn,look,easy

Author

R. J. Mathar, Jul 21 2016

Status

approved