cp's OEIS Frontend

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

%I A053570 #24 May 31 2018 02:12:48
%S A053570 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 A053570 156,125,164,137,242,113,278,213,230,217,272,191,396,275,320,261,490,
%U A053570 237,542,369,386,401,650,355,640,431,560,507,830,449,704,551,696,643
%N A053570 Sum of totient functions over arguments running through reduced residue system of n.
%C A053570 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 A053570 Equals row sums of triangle A143620. - _Gary W. Adamson_, Aug 27 2008
%H A053570 T. D. Noe, <a href="/A053570/b053570.txt">Table of n, a(n) for n = 1..1000</a>
%F A053570 a(n) = Sum_{k>=1} A000010(A038566(n,k)). - _R. J. Mathar_, Jan 09 2017
%e A053570 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 A053570 A038566_row := proc(n)
%p A053570     a := {} ;
%p A053570     for m from 1 to n do
%p A053570         if igcd(n,m) =1 then
%p A053570             a := a union {m} ;
%p A053570         end if;
%p A053570     end do:
%p A053570     a ;
%p A053570 end proc:
%p A053570 A053570 := proc(n)
%p A053570     add(numtheory[phi](r),r=A038566_row(n)) ;
%p A053570 end proc:
%p A053570 seq(A053570(n),n=1..30) ; # _R. J. Mathar_, Jan 09 2017
%t A053570 Join[{1}, Table[Sum[EulerPhi[i] * KroneckerDelta[GCD[i, n], 1], {i, n - 1}], {n, 2, 60}]] (* _Alonso del Arte_, Nov 02 2014 *)
%Y A053570 Cf. A000010, A002088.
%Y A053570 Cf. A143620. - _Gary W. Adamson_, Aug 27 2008
%K A053570 nonn
%O A053570 1,3
%A A053570 _Labos Elemer_, Jan 17 2000