A342594 Earliest occurrence of the next distinct width pattern (as listed in A342592) in the symmetric representation of sigma(n) not yet encountered as n increases.

1, 3, 6, 9, 15, 18, 21, 30, 45, 60, 63, 72, 75, 78, 81, 90, 105, 120, 135, 147, 150, 162, 165, 180, 189, 210, 225, 231, 300, 315, 357, 360, 378, 390, 405, 420, 441, 450, 465, 495, 504, 525, 540, 567, 630, 648, 666, 675, 690, 693, 729, 735, 770, 810, 825, 840, 855, 858, 882, 900, 903, 945, 975, 990

Offset: 1

Author

Hartmut F. W. Hoft, Mar 16 2021

Keywords

• nonn

Comments

The width pattern of the symmetric representation of sigma(a(n)) is the n-th row of the table of A342592.

Conjecture: If for some number n the symmetric representation of sigma(n) has the symmetric width pattern w in row n of A342592 then infinitely many numbers have that width pattern w.

Examples

			a(1) = 1 is the smallest power of 2 whose symmetric representation of sigma has width pattern (1).
a(2) = 3 is the smallest odd prime whose symmetric representation of sigma has width pattern (1 0 1).
a(4) = 9 is the first number whose symmetric representation of sigma has width pattern (1 0 1 0 1). The infinitely many numbers 2^s * p^2, s >= 0 and p an odd prime larger than 2^(s+1), have the same width pattern.
		

Crossrefs

Cf. A235791, A237048, A237270, A237591, A237593, A249223, A341969, A342592.

Programs

Mathematica

(* function a341969[ ] is defined in A341969 *)
a342594[n_] := Module[{listW={}, listK={}, k, w}, For[k=1, k<=n, k++, w=a341969[k]; If[!MemberQ[listW, w], AppendTo[listW, w]; AppendTo[listK, k]]]; listK]
a342594[990] (* 64 entries; the 64th new pattern is encountered at n=990 *)