OFFSET
1,1
COMMENTS
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.
EXAMPLE
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.
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.
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:
6 | 1 3 1 2
12 | 1 3 1 2
15 | 1 2 3 5 1 0 1 2
18 | 1 3 4 1 2 1
20 | 1 5 1 2
24 | 1 3 1 2
28 | 1 7 1 2
30 | 1 3 4 5 1 2 1 2
35 | 1 2 5 7 1 0 1 2
36 | 1 3 8 1 2 1
...
MATHEMATICA
eP[n_] := If[EvenQ[n], FactorInteger[n][[1, 2]], 0]+1
sDiv[n_] := Module[{d=Select[Divisors[n], OddQ]}, Select[Union[d, d*2^eP[n]], #<=row[n]&]]
mW2Q[n_] := Max[FoldWhileList[#1+If[OddQ[#2], 1, -1]&, sDiv[n], #1<=2&]]==2
a375611[m_, n_] := Select[Range[m, n], mW2Q]
a375611[1, 200]
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Aug 21 2024
STATUS
approved