|
| |
|
|
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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
2,4
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
a(8) = (1 + 1/3)*1*3 = 4 because 1 and 3 are those positive integers <= 8/2 and coprime to 8.
|
|
|
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])):
|
|
|
MATHEMATICA
|
a[n_] := Module[{r = Range[Floor[n/2]], s}, s = Select[r, GCD[#, n]==1&]; Total[1/s] Times @@ s];
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
