login
A241559
Largest part of the symmetric representation of sigma(n).
8
1, 3, 2, 7, 3, 12, 4, 15, 5, 9, 6, 28, 7, 12, 8, 31, 9, 39, 10, 42, 11, 18, 12, 60, 13, 21, 14, 56, 15, 72, 16, 63, 17, 27, 18, 91, 19, 30, 20, 90, 21, 96, 22, 42, 32, 36, 24, 124, 25, 39, 26, 49, 27, 120, 28, 120, 29, 45, 30, 168, 31, 48, 32, 127
OFFSET
1,2
COMMENTS
First differs from A241838 at a(45).
If A237271(n) = 1 then a(n) = A241558(n) = A241838(n) = A000203(n).
If n is an odd prime then a(n) = (n + 1)/2 = A241558(n) = A241838(n).
For more information see A237593.
EXAMPLE
For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
y
.
._ _ _ _ _ 5
|_ _ _ _ _|
. |_ _ 3
. |_ |
. |_|_ _ 5
. | |
. | |
. | |
. | |
. . . . . . . . |_| . . x
.
There are three parts [5, 3, 5] and the largest part is 5 so a(9) = 5.
For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23] and the largest part is 32 so a(45) = 32.
MATHEMATICA
(* Function a237270[] is defined in A237270 *)
a241559[n_]:=Max[a237270[n]]
Map[a241559, Range[64]] (* data *)
(* Hartmut F. W. Hoft, Sep 19 2014 *)
KEYWORD
nonn
AUTHOR
Michel Marcus and Omar E. Pol, Apr 29 2014
STATUS
approved