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A056188 a(1) = 1; for n>1, sum of binomial(n,k) as k runs over RRS(n), the reduced residue system of n. 4
1, 2, 6, 8, 30, 12, 126, 128, 342, 260, 2046, 1608, 8190, 4760, 15840, 32768, 131070, 80820, 524286, 493280, 1165542, 1391720, 8388606, 5769552, 26910650, 23153832, 89478486, 131849648, 536870910, 352845960, 2147483646, 2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is a multiple of n for all n.

LINKS

Table of n, a(n) for n=1..32.

Laszlo Toth, Weighted gcd-sum functions, J. Integer Sequences, 14 (2011), Article 11.7.7

FORMULA

a(n)= Sum{binomial[n, k]; GCD[n, k]=1, 0<=k<=n}

EXAMPLE

For n=prime, a(n)=2^n-2 because all k<=n except 0 and n are used; n=10, RRS[10]={1,3,7,9}, the corresponding coefficients are {10,120,120,10}, so the sum a(10)=260.

MAPLE

A056188 := proc(n)

    a := 0 ;

    for k from 1 to n do

        if igcd(k, n) = 1 then

            a := a+binomial(n, k);

        end if ;

    end do:

    a ;

end proc: # R. J. Mathar, Sep 02 2017

MATHEMATICA

f[n_] := Plus @@ Binomial[n, Select[ Range[n], GCD[n, # ] == 1 &]]; Table[ f[n], {n, 33}] (* Robert G. Wilson v, Nov 04 2004 *)

CROSSREFS

Cf. A056045, A056189.

Sequence in context: A272614 A210737 A140539 * A020696 A290249 A321471

Adjacent sequences:  A056185 A056186 A056187 * A056189 A056190 A056191

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 02 2000

STATUS

approved

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Last modified May 25 05:45 EDT 2019. Contains 323539 sequences. (Running on oeis4.)