A241838 Column 1 of A237270, also the right border.

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, 23, 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 A241559 at a(45).

If A237271(n) = 1 then a(n) = A241558(n) = A241559(n) = A000203(n).

If n is an odd prime then a(n) = (n + 1)/2 = A241558(n) = A241559(n).

For more information see A237593.

Links

Robert Price, Table of n, a(n) for n = 1..10000

Formula

a(n) = A237270(n, 1) = A237270(n, A237271(n)).

Example

For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23], both the first and the last term are equal to 23, so a(45) = 23.

Mathematica

Map[First[a237270[#]]&, Range[64]] (* data : computing all parts *)
(* computing only the first part of the symmetric representation of sigma(n) *)
row[n_] := Floor[(Sqrt[8n+1]-1)/2] (* in A237591 *)
f[n_, k_] := If[Mod[n-k*(k+1)/2, k]==0, (-1)^(k+1), 0]
g[n_, k_] := Ceiling[(n+1)/k-(k+1)/2] - Ceiling[(n+1)/(k+1)-(k+2)/2] (* in A237591 *)
a241838[n_] := Module[{r=row[n], widths={}, i=1, w=0, len, legs}, w+=f[n, i]; While[i<=r && w!=0, AppendTo[widths, w]; i++; w+=f[n, i]]; len=Length[widths]; legs=Map[g[n, #]&, Range[len]]; If[len<r, widths.legs, 2*widths.legs-Last[widths]]]
Map[a241838, Range[64]] (* data *)
(* Hartmut F. W. Hoft, Jan 25 2018 *)

Crossrefs

Cf. A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241558, A241559, A245092, A262626.

Sequence in context: A296512 A241558 A295422 * A241559 A165794 A075270

Adjacent sequences: A241835 A241836 A241837 * A241839 A241840 A241841

Keyword

nonn,look

Author

Omar E. Pol, Apr 29 2014

Status

approved