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A275258 Toth's partial sum over the number of divisors of the greatest unitary divisor. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

FORMULA

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

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. A165430.

Sequence in context: A053158 A206924 A185443 * A230593 A304411 A332619

Adjacent sequences:  A275255 A275256 A275257 * A275259 A275260 A275261

KEYWORD

nonn,look,easy

AUTHOR

R. J. Mathar, Jul 21 2016

STATUS

approved

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Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)