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A053570 Sum of totient functions over arguments running through reduced residue system of n. 8
1, 1, 2, 3, 6, 5, 12, 13, 18, 15, 32, 21, 46, 35, 42, 49, 80, 49, 102, 71, 88, 85, 150, 89, 156, 125, 164, 137, 242, 113, 278, 213, 230, 217, 272, 191, 396, 275, 320, 261, 490, 237, 542, 369, 386, 401, 650, 355, 640, 431, 560, 507, 830, 449, 704, 551, 696, 643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Phi summation results over numbers not exceeding n are given in A002088 while summation over the divisor set of n would give n. This is a further way of Phi summation.

Equals row sums of triangle A143620. - Gary W. Adamson, Aug 27 2008

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{k>=1} A000010(A038566(n,k)). - R. J. Mathar, Jan 09 2017

EXAMPLE

Given n = 36, its reduced residue system is {1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35}; the Euler phi of these terms are {1, 4, 6, 10, 12, 16, 18, 22, 20, 28, 30, 24}. Summation over this last set gives 191. So a(36) = 191.

MAPLE

A038566_row := proc(n)

    a := {} ;

    for m from 1 to n do

        if igcd(n, m) =1 then

            a := a union {m} ;

        end if;

    end do:

    a ;

end proc:

A053570 := proc(n)

    add(numtheory[phi](r), r=A038566_row(n)) ;

end proc:

seq(A053570(n), n=1..30) ; # R. J. Mathar, Jan 09 2017

MATHEMATICA

Join[{1}, Table[Sum[EulerPhi[i] * KroneckerDelta[GCD[i, n], 1], {i, n - 1}], {n, 2, 60}]] (* Alonso del Arte, Nov 02 2014 *)

CROSSREFS

Cf. A000010, A002088.

Cf. A143620. - Gary W. Adamson, Aug 27 2008

Sequence in context: A095113 A002517 A253568 * A129647 A225652 A136183

Adjacent sequences:  A053567 A053568 A053569 * A053571 A053572 A053573

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 17 2000

STATUS

approved

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)