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.

1, 1, 1, 3, 1, 11, 4, 14, 4, 274, 6, 1764, 23, 106, 176, 109584, 47, 1026576, 300, 6960, 1689, 120543840, 552, 26854848, 19524, 7962160, 34986, 283465647360, 1312, 4339163001600, 4098240, 164944640, 4098240, 13833580032, 133542, 22376988058521600, 71697105

Offset: 2

Author

Leroy Quet, Nov 13 2004

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..900

Crossrefs

Cf. A056855.

Programs

Maple

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
# second Maple program:
a:= n-> (l-> mul(i, i=l)*add(1/i, i=l))(
         select(x-> igcd(x, n)=1, [$1..n/2])):
seq(a(n), n=2..40);  # Alois P. Heinz, May 22 2015

Mathematica

a[n_] := Module[{r = Range[Floor[n/2]], s}, s = Select[r, GCD[#, n]==1&]; Total[1/s] Times @@ s];
a /@ Range[2, 40] (* Jean-François Alcover, Nov 18 2020 *)

Extensions

More terms from Emeric Deutsch, Apr 22 2006