A241559 Largest part of the symmetric representation of sigma(n).

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

Author

Michel Marcus and Omar E. Pol, Apr 29 2014

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241558, A071561, A071562, A241838.

Programs

Mathematica

(* Function a237270[] is defined in A237270 *)
a241559[n_]:=Max[a237270[n]]
Map[a241559,Range[64]] (* data *)
(* Hartmut F. W. Hoft, Sep 19 2014 *)