A347528 Total number of layers of width 1 of all symmetric representations of sigma() with subparts of all positive integers <= n.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 38, 39, 40, 41, 42, 44, 46, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 72, 73, 74, 75, 78, 79, 80, 82, 83, 84, 86, 87, 88

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

For the first five positive integers every symmetric representation of sigma() with subparts has only one layer of width 1, so a(5) = 1 + 1 + 1 + 1 + 1 = 5.
For n = 6 the symmetric representation of sigma(6) with subparts has two layers of width 1 as shown below:
                     _ _ _ _
                    |_ _ _  |_
                          | |_|_
                          |_ _  |
                              | |
                              | |
                              |_|
So a(6) = 5 + 2 = 7.

Mathematica

Accumulate@ Map[Max@ Accumulate[#] &, Table[If[OddQ[k], Boole@ Divisible[n, k], -Boole@ Divisible[n - k/2, k]], {n, 68}, {k, Floor[(Sqrt[8 n + 1] - 1)/2]}]] (* Michael De Vlieger, Oct 27 2021 *)

Crossrefs

Partial sums of A250068.

Cf. A196020, A235791, A236104, A237270, A237271, A237591, A237590, A237593, A279387, A279391, A279667, A280850, A280851, A296508.

Sequence in context: A109234 A335137 A267304 * A002855 A303234 A175233

Adjacent sequences: A347525 A347526 A347527 * A347529 A347530 A347531

Keyword

nonn

Author

Omar E. Pol, Sep 05 2021

Status

approved