This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375611 #18 Sep 06 2024 20:19:44
%S A375611 6,12,15,18,20,24,28,30,35,36,40,42,45,48,54,56,63,66,70,75,77,78,80,
%T A375611 88,91,96,99,100,102,104,105,108,110,112,114,117,130,132,135,138,143,
%U A375611 150,153,154,156,160,162,165,170,174,175,176,182,186,187,189,190,192,195,196,200
%N A375611 Numbers k whose symmetric representation of sigma(k) has at least a part with maximum width 2.
%C A375611 Number m = 2^k * q, k >= 0 and q odd, is in this sequence precisely when for any divisor s <= A003056(m) of q there is at most one divisor t of q satisfying s < t <= min(2^(k+1) * s, A003056(m)), and at least one such pair s < t of successive odd divisors exists. Equivalently, row m of the triangle in A249223 contains at least one 2, but no number larger than 2.
%e A375611 a(4) = 18 has width pattern 1 2 1 2 1 in its symmetric representation of sigma consisting of a single part, and row 18 in the triangle of A249223 is 1 1 2 1 1.
%e A375611 a(9) = 35 has width pattern 1 0 1 2 1 0 1 in its symmetric representation of sigma consisting of 3 parts, and row 35 in the triangle of A249223 is 1 0 0 0 1 1 2.
%e A375611 Irregular triangle of rows a(n) in triangle of A341970, i.e. of positions of 1's in triangle of A237048, and for the corresponding widths to the diagonal in triangle of A341969:
%e A375611 a(n)| row in A341970 left half of row in A341969
%e A375611 6 | 1 3 1 2
%e A375611 12 | 1 3 1 2
%e A375611 15 | 1 2 3 5 1 0 1 2
%e A375611 18 | 1 3 4 1 2 1
%e A375611 20 | 1 5 1 2
%e A375611 24 | 1 3 1 2
%e A375611 28 | 1 7 1 2
%e A375611 30 | 1 3 4 5 1 2 1 2
%e A375611 35 | 1 2 5 7 1 0 1 2
%e A375611 36 | 1 3 8 1 2 1
%e A375611 ...
%t A375611 eP[n_] := If[EvenQ[n], FactorInteger[n][[1, 2]], 0]+1
%t A375611 sDiv[n_] := Module[{d=Select[Divisors[n], OddQ]}, Select[Union[d, d*2^eP[n]], #<=row[n]&]]
%t A375611 mW2Q[n_] := Max[FoldWhileList[#1+If[OddQ[#2], 1, -1]&, sDiv[n], #1<=2&]]==2
%t A375611 a375611[m_, n_] := Select[Range[m, n], mW2Q]
%t A375611 a375611[1, 200]
%Y A375611 Column 2 of A253258.
%Y A375611 Subsequence of A005279.
%Y A375611 Some subsequences are A352030, A370205, A370206, A370209.
%Y A375611 Cf. A003056, A174905, A235791, A237593, A249223, A249351, A250068, A341969, A341970.
%K A375611 nonn
%O A375611 1,1
%A A375611 _Hartmut F. W. Hoft_, Aug 21 2024