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

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, 0, 136, 0, 80, 82, 110, 78, 170, 0, 138, 116, 190, 0, 264, 0, 192, 198, 204, 0, 310, 66, 294, 196, 272, 0, 398, 182, 358, 248, 328, 0, 584, 0, 372, 372, 372, 248, 658, 0, 468

Offset: 1

Author

Labos Elemer, Jan 17 2000

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002088, A045763.

Programs

Maple

A045763_row :=proc(n)
    a := {} ;
    dvs := numtheory[divisors](n) ;
    for m from 2 to n-1 do
        if igcd(m,n) >1 and not m in dvs then
            a := a union {m} ;
        end if;
    end do:
    a;
end proc:
A053571 := proc(n)
    add(numtheory[phi](a), a=A045763_row(n)) ;
end proc: # R. J. Mathar, Jan 09 2017

Mathematica

Table[Total@ EulerPhi@ Select[Range@ n, 1 < GCD[#, n] < # &], {n, 68}] (* Michael De Vlieger, Mar 05 2017 *)