A053570 Sum of totient functions over arguments running through reduced residue system of n.

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

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: A367584 A002517 A253568 * A129647 A225652 A136183

Adjacent sequences: A053567 A053568 A053569 * A053571 A053572 A053573

Keyword

nonn

Author

Labos Elemer, Jan 17 2000

Status

approved