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

1,2

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.

Links

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

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 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.

Mathematica

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

Crossrefs

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

Sequence in context: A324509 A335653 A296512 * A295422 A241838 A241559

Adjacent sequences: A241555 A241556 A241557 * A241559 A241560 A241561

Keyword

nonn

Author

Michel Marcus and Omar E. Pol, Apr 29 2014

Extensions

More terms from Jinyuan Wang, Feb 14 2020

Status

approved