cp's OEIS Frontend

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

%I A347528 #18 Oct 28 2021 02:01:55
%S A347528 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,
%T A347528 32,33,35,36,38,39,40,41,42,44,46,47,48,49,51,52,54,55,56,58,59,60,62,
%U A347528 63,64,65,66,67,69,70,72,73,74,75,78,79,80,82,83,84,86,87,88
%N A347528 Total number of layers of width 1 of all symmetric representations of sigma() with subparts of all positive integers <= n.
%H A347528 Michael De Vlieger, <a href="/A347528/b347528.txt">Table of n, a(n) for n = 1..10000</a>
%e A347528 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.
%e A347528 For n = 6 the symmetric representation of sigma(6) with subparts has two layers of width 1 as shown below:
%e A347528                      _ _ _ _
%e A347528                     |_ _ _  |_
%e A347528                           | |_|_
%e A347528                           |_ _  |
%e A347528                               | |
%e A347528                               | |
%e A347528                               |_|
%e A347528 So a(6) = 5 + 2 = 7.
%t A347528 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 *)
%Y A347528 Partial sums of A250068.
%Y A347528 Cf. A196020, A235791, A236104, A237270, A237271, A237591, A237590, A237593, A279387, A279391, A279667, A280850, A280851, A296508.
%K A347528 nonn
%O A347528 1,2
%A A347528 _Omar E. Pol_, Sep 05 2021