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%I #13 Mar 06 2017 03:48:32
%S 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 0,136,0,80,82,110,78,170,0,138,116,190,0,264,0,192,198,204,0,310,66,
%U 294,196,272,0,398,182,358,248,328,0,584,0,372,372,372,248,658,0,468
%N Sum of totient functions over arguments running through numbers unrelated to n.
%C 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 Michael De Vlieger, <a href="/A053571/b053571.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 A045763_row :=proc(n)
%p a := {} ;
%p dvs := numtheory[divisors](n) ;
%p for m from 2 to n-1 do
%p if igcd(m,n) >1 and not m in dvs then
%p a := a union {m} ;
%p end if;
%p end do:
%p a;
%p end proc:
%p A053571 := proc(n)
%p add(numtheory[phi](a), a=A045763_row(n)) ;
%p end proc: # _R. J. Mathar_, Jan 09 2017
%t Table[Total@ EulerPhi@ Select[Range@ n, 1 < GCD[#, n] < # &], {n, 68}] (* _Michael De Vlieger_, Mar 05 2017 *)
%Y Cf. A000010, A002088, A045763.
%K nonn
%O 1,6
%A _Labos Elemer_, Jan 17 2000
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