OFFSET
1
COMMENTS
Terms m in A126706 are of the form p^2*k with p prime and k not a power of p. Therefore, m occurs densely in the residues r mod q = p^2*k where k <= q/p^2 for p|q, and q = A002110(j)^2 (i.e., q in A061742), only interrupted by perfect powers of p. Using this principle we can produce a sieve-like diagram for this sequence as shown in the example. - Michael De Vlieger, Jul 15 2022
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..100000
Michael De Vlieger, Color-coded diagram arranging n = 1..1296 mod 36, showing primes in red, composite prime powers (A246547) in gold, and composite squarefree numbers (A120944) in green). Products of composite prime powers (A286708) are shown in magenta; A286708 is a subset of A126706; these and the numbers in blue comprise terms in A126706.
Michael De Vlieger, Raster (i*j) with i = j = 1..900, showing (900i + j) as black if in A126706, otherwise white. Effectively an image of this sequence mod 900. Contains 810000 terms of this sequence.
Michael De Vlieger, Ulam-style spiral arrangement of a(n) for n = 1..229441. The evident "chatter" relates to 2^2*k with k not a power of 2.
EXAMPLE
From Michael De Vlieger, Jul 15 2022: (Start)
This sequence arranged in 18 rows of 36 terms m, replacing 0 with "*" for composite prime powers m, otherwise "." so as to clarify the pattern:
...*...**..1...*.1.1...1*.*1...*...1
...1...11..1*1.1.1.1...1..1*...1...1
..11...1*..1...1.1.1...1.111...1...1
...1...11..1*..1*1.*...1..11...1...1
..11.1.11..1...1.1.1...1*.11..11...1
...1...11..1...1.1.1...1..11...1...1
...1...11..1...1.1.1...1.1*11..1.1.1
...*...11..1...1.1.1..11..11...1...1
*..1.1.11..1...1.1.1...1..11...1...1
1..1...11..1.1.1.1*1...1.111...1...1
*.11...11..1..11.1.1...1..11...1...1
...1...11..1...1.1.1...1..111..1...1
...1...11..1...1.1.1...1..11...1...1
...1..111..1...1.1.1.1.1..11...1...1
..11...*1..1...1.1.11..1*.11...1..11
...1...111.1...1.1.1...1..11...1..11
.1.1...11..1...1.1.1...1..111..1...1
...1...11..1*..1.1.1...11.11...1...1 (End)
MATHEMATICA
a[n_] := If[SquareFreeQ[n] || PrimePowerQ[n], 0, 1]; Array[a, 100] (* Amiram Eldar, Jul 14 2022 *)
(* Read up to 810000 terms from the 900 X 900 raster image *)
With[{m = 4}, Flatten[ImageData["https://oeis.org/A355447/a355447_1.png"][[1 ;; m]] /. {1. -> 0, 0. -> 1}] (* Michael De Vlieger, Jul 15 2022 *)
PROG
(PARI) A355447(n) = ((omega(n)>1) && !issquarefree(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 13 2022
STATUS
approved