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a(n) = (Sum 1/k) (Product k), where both the sum and product are over those k where 1 <= k <= n/2 and gcd(k,n) = 1.
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%I #19 Nov 18 2020 06:50:56

%S 1,1,1,3,1,11,4,14,4,274,6,1764,23,106,176,109584,47,1026576,300,6960,

%T 1689,120543840,552,26854848,19524,7962160,34986,283465647360,1312,

%U 4339163001600,4098240,164944640,4098240,13833580032,133542,22376988058521600,71697105

%N a(n) = (Sum 1/k) (Product k), where both the sum and product are over those k where 1 <= k <= n/2 and gcd(k,n) = 1.

%H Alois P. Heinz, <a href="/A099001/b099001.txt">Table of n, a(n) for n = 2..900</a>

%e a(8) = (1 + 1/3)*1*3 = 4 because 1 and 3 are those positive integers <= 8/2 and coprime to 8.

%p b:=proc(n) local B,k: B:={}: for k from 1 to n/2 do if gcd(k,n)=1 then B:=B union {k} else B:=B fi od end: a:=proc(n) add(1/b(n)[j],j=1..nops(b(n)))*product(b(n)[j],j=1..nops(b(n))) end: seq(a(n),n=2..40); # _Emeric Deutsch_, Apr 22 2006

%p # second Maple program:

%p a:= n-> (l-> mul(i, i=l)*add(1/i, i=l))(

%p select(x-> igcd(x, n)=1, [$1..n/2])):

%p seq(a(n), n=2..40); # _Alois P. Heinz_, May 22 2015

%t a[n_] := Module[{r = Range[Floor[n/2]], s}, s = Select[r, GCD[#, n]==1&]; Total[1/s] Times @@ s];

%t a /@ Range[2, 40] (* _Jean-François Alcover_, Nov 18 2020 *)

%Y Cf. A056855.

%K nonn

%O 2,4

%A _Leroy Quet_, Nov 13 2004

%E More terms from _Emeric Deutsch_, Apr 22 2006