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A053571 Sum of totient functions over arguments running through numbers unrelated to n.

%I A053571 #13 Mar 06 2017 03:48:32
%S A053571 0,0,0,0,0,2,0,2,2,8,0,14,0,16,16,16,0,36,0,38,32,44,0,68,20,62,40,78,
%T A053571 0,136,0,80,82,110,78,170,0,138,116,190,0,264,0,192,198,204,0,310,66,
%U A053571 294,196,272,0,398,182,358,248,328,0,584,0,372,372,372,248,658,0,468
%N A053571 Sum of totient functions over arguments running through numbers unrelated to n.
%C A053571 Phi-summation over numbers not exceeding n are given in A002088, over divisor-set of n would give n, over RRS or unrelated numbers to n give newer values: at n=36 these values are {396,36,191,170}. This is a further way of Phi-summation.
%H A053571 Michael De Vlieger, <a href="/A053571/b053571.txt">Table of n, a(n) for n = 1..10000</a>
%e A053571 n=36 and its "unrelated-set" is {8,10,14,15,16,20,21,22,24,26,27,28,30,32,33,34} and their totients are {4,4,6,8,8,8,12,10,8,12,18,12,8,16,20,16}. The sum of these values is 170, so a(36)=170. For primes the unrelated set is empty and Phi-sum over empty set is 0.
%p A053571 A045763_row :=proc(n)
%p A053571     a := {} ;
%p A053571     dvs := numtheory[divisors](n) ;
%p A053571     for m from 2 to n-1 do
%p A053571         if igcd(m,n) >1 and not m in dvs then
%p A053571             a := a union {m} ;
%p A053571         end if;
%p A053571     end do:
%p A053571     a;
%p A053571 end proc:
%p A053571 A053571 := proc(n)
%p A053571     add(numtheory[phi](a), a=A045763_row(n)) ;
%p A053571 end proc: # _R. J. Mathar_, Jan 09 2017
%t A053571 Table[Total@ EulerPhi@ Select[Range@ n, 1 < GCD[#, n] < # &], {n, 68}] (* _Michael De Vlieger_, Mar 05 2017 *)
%Y A053571 Cf. A000010, A002088, A045763.
%K A053571 nonn
%O A053571 1,6
%A A053571 _Labos Elemer_, Jan 17 2000