A241558 Smallest part of the symmetric representation of sigma(n).

1, 3, 2, 7, 3, 12, 4, 15, 3, 9, 6, 28, 7, 12, 8, 31, 9, 39, 10, 42, 5, 18, 12, 60, 5, 21, 6, 56, 15, 72, 16, 63, 7, 27, 12, 91, 19, 30, 8, 90, 21, 96, 22, 42, 23, 36, 24, 124, 7, 15, 10, 49, 27, 120, 8, 120, 11, 45, 30, 168, 31, 48, 12, 127, 9, 144, 34, 63, 13

Offset: 1

Author

Michel Marcus and Omar E. Pol, Apr 29 2014

Keywords

• nonn

Comments

If A237271(n) = 1 then a(n) = A241559(n) = A241838(n) = A000203(n).

If n is an odd prime then a(n) = (n + 1)/2 = A241559(n) = A241838(n).

For more information see A237270 and 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 smallest part is 3 so a(9) = 3.
For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23] and the smallest part is 23 so a(45) = 23.
For n = 63 the symmetric representation of sigma(63) = 104 has five parts [32, 12, 16, 12, 32] and the smallest part is 12 so a(63) = 12.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241559, A241838, A245092, A262626.

Programs

Mathematica

(* Function a237270[] is defined in A237270 *)
a241558[n_]:=Min[a237270[n]]
Map[a241558,Range[64]] (* data *)
(* Hartmut F. W. Hoft, Sep 19 2014 *)

Extensions

More terms from Jinyuan Wang, Feb 14 2020