This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303431 Aperiodic tree numbers. Matula-Goebel numbers of aperiodic rooted trees. 38
 1, 2, 3, 5, 6, 10, 11, 12, 13, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 37, 39, 40, 41, 44, 45, 47, 48, 50, 52, 54, 55, 58, 60, 61, 62, 65, 66, 71, 72, 74, 75, 78, 79, 80, 82, 87, 88, 89, 90, 93, 94, 96, 99, 101, 104, 108, 109, 110, 111, 113, 116, 117, 120, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A positive integer is an aperiodic tree number iff either it is equal to 1 or it belongs to A007916 (numbers that are not perfect powers, or numbers whose prime multiplicities are relatively prime) and all of its prime indices are also aperiodic tree numbers, where a prime index of n is a number m such that prime(m) divides n. LINKS EXAMPLE Sequence of aperiodic rooted trees begins: 01 o 02 (o) 03 ((o)) 05 (((o))) 06 (o(o)) 10 (o((o))) 11 ((((o)))) 12 (oo(o)) 13 ((o(o))) 15 ((o)((o))) 18 (o(o)(o)) 20 (oo((o))) 22 (o(((o)))) 24 (ooo(o)) 26 (o(o(o))) 29 ((o((o)))) 30 (o(o)((o))) 31 (((((o))))) 33 ((o)(((o)))) MATHEMATICA zapQ[1]:=True; zapQ[n_]:=And[GCD@@FactorInteger[n][[All, 2]]===1, And@@zapQ/@PrimePi/@FactorInteger[n][[All, 1]]]; Select[Range[100], zapQ] CROSSREFS Cf. A000081, A000740, A000837, A007097, A007916, A052409, A052410, A061775, A111299, A214577, A275024, A276625, A290760, A290822, A291442, A298533, A298536, A301700, A302242, A303386. Sequence in context: A162309 A014593 A261088 * A317709 A034044 A047447 Adjacent sequences:  A303428 A303429 A303430 * A303432 A303433 A303434 KEYWORD nonn AUTHOR Gus Wiseman, Apr 23 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)