login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A316794 Matula-Goebel numbers of aperiodic rooted trees with locally distinct multiplicities. 4
1, 2, 3, 5, 11, 12, 18, 20, 24, 31, 37, 40, 44, 45, 48, 50, 54, 61, 71, 72, 75, 80, 88, 89, 96, 99, 108, 124, 127, 135, 148, 157, 160, 162, 173, 176, 192, 193, 197, 200, 223, 229, 242, 244, 248, 250, 251, 275, 279, 283, 284, 288, 296, 297, 320, 333, 352, 353 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A positive integer belongs to the sequence 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) as well as to A130091 (numbers whose prime multiplicities are distinct), and all of its prime indices already belong to the sequence. A prime index of n is a number m such that prime(m) divides n.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Sequence of aperiodic rooted trees with locally distinct multiplicities preceded by their Matula-Goebel numbers begins:

   1: o

   2: (o)

   3: ((o))

   5: (((o)))

  11: ((((o))))

  12: (oo(o))

  18: (o(o)(o))

  20: (oo((o)))

  24: (ooo(o))

  31: (((((o)))))

  37: ((oo(o)))

  40: (ooo((o)))

  44: (oo(((o))))

  45: ((o)(o)((o)))

  48: (oooo(o))

  50: (o((o))((o)))

MATHEMATICA

mgsbQ[n_]:=Or[n==1, And[UnsameQ@@Last/@FactorInteger[n], GCD@@Last/@FactorInteger[n]==1, And@@Cases[FactorInteger[n], {p_, _}:>mgsbQ[PrimePi[p]]]]];

Select[Range[100], mgsbQ]

CROSSREFS

Cf. A000081, A004111, A007097, A007916, A061775, A276625, A301700  A303431, A316793, A316795, A316796.

Sequence in context: A210144 A243357 A066159 * A103027 A093902 A269004

Adjacent sequences:  A316791 A316792 A316793 * A316795 A316796 A316797

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 14 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 02:12 EST 2020. Contains 338756 sequences. (Running on oeis4.)