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A099001 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.

%I A099001 #19 Nov 18 2020 06:50:56
%S A099001 1,1,1,3,1,11,4,14,4,274,6,1764,23,106,176,109584,47,1026576,300,6960,
%T A099001 1689,120543840,552,26854848,19524,7962160,34986,283465647360,1312,
%U A099001 4339163001600,4098240,164944640,4098240,13833580032,133542,22376988058521600,71697105
%N A099001 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 A099001 Alois P. Heinz, <a href="/A099001/b099001.txt">Table of n, a(n) for n = 2..900</a>
%e A099001 a(8) = (1 + 1/3)*1*3 = 4 because 1 and 3 are those positive integers <= 8/2 and coprime to 8.
%p A099001 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 A099001 # second Maple program:
%p A099001 a:= n-> (l-> mul(i, i=l)*add(1/i, i=l))(
%p A099001          select(x-> igcd(x, n)=1, [$1..n/2])):
%p A099001 seq(a(n), n=2..40);  # _Alois P. Heinz_, May 22 2015
%t A099001 a[n_] := Module[{r = Range[Floor[n/2]], s}, s = Select[r, GCD[#, n]==1&]; Total[1/s] Times @@ s];
%t A099001 a /@ Range[2, 40] (* _Jean-François Alcover_, Nov 18 2020 *)
%Y A099001 Cf. A056855.
%K A099001 nonn
%O A099001 2,4
%A A099001 _Leroy Quet_, Nov 13 2004
%E A099001 More terms from _Emeric Deutsch_, Apr 22 2006