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A241838 Column 1 of A237270, also the right border. 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, 23, 36, 24, 124, 25, 39, 26, 49, 27, 120, 28, 120, 29, 45, 30, 168, 31, 48, 32, 127 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)