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

Author

Labos Elemer, Jan 17 2000

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000010, A002088.

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

Programs

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 *)

Formula

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