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A053571 Sum of totient functions over arguments running through numbers unrelated to n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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.

LINKS

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000010, A002088, A045763.

Sequence in context: A284570 A256847 A046277 * A129883 A293578 A098489

Adjacent sequences:  A053568 A053569 A053570 * A053572 A053573 A053574

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 17 2000

STATUS

approved

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)