A053570 - OEIS

%I #24 May 31 2018 02:12:48

%S 1,1,2,3,6,5,12,13,18,15,32,21,46,35,42,49,80,49,102,71,88,85,150,89,

%T 156,125,164,137,242,113,278,213,230,217,272,191,396,275,320,261,490,

%U 237,542,369,386,401,650,355,640,431,560,507,830,449,704,551,696,643

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

%C 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.

%C Equals row sums of triangle A143620. - _Gary W. Adamson_, Aug 27 2008

%H T. D. Noe, <a href="/A053570/b053570.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{k>=1} A000010(A038566(n,k)). - _R. J. Mathar_, Jan 09 2017

%e 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.

%p A038566_row := proc(n)

%p     a := {} ;

%p     for m from 1 to n do

%p         if igcd(n,m) =1 then

%p             a := a union {m} ;

%p         end if;

%p     end do:

%p     a ;

%p end proc:

%p A053570 := proc(n)

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

%p end proc:

%p seq(A053570(n),n=1..30) ; # _R. J. Mathar_, Jan 09 2017

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

%Y Cf. A000010, A002088.

%Y Cf. A143620. - _Gary W. Adamson_, Aug 27 2008

%K nonn

%O 1,3

%A _Labos Elemer_, Jan 17 2000