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Revision History for A316794

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A316794

Matula-Goebel numbers of aperiodic rooted trees with locally distinct multiplicities.
(history; published version)

#11 by Susanna Cuyler at Tue Dec 25 17:28:35 EST 2018

STATUS

proposed

approved

#10 by Michel Marcus at Tue Dec 25 12:22:57 EST 2018

STATUS

editing

proposed

#9 by Michel Marcus at Tue Dec 25 12:22:53 EST 2018

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 the sequence. A prime index of n is a number m such that prime(m) divides n.

STATUS

approved

editing

#8 by N. J. A. Sloane at Sun Jul 15 13:25:28 EDT 2018

STATUS

proposed

approved

#7 by Gus Wiseman at Sat Jul 14 22:25:54 EDT 2018

STATUS

editing

proposed

#6 by Gus Wiseman at Sat Jul 14 14:01:47 EDT 2018

CROSSREFS

Cf. A000081, A000837, A004111, A007097, A007916, A061775, A276625, A277098, A301700 A303431, A316793, A316795, A316796.

#5 by Gus Wiseman at Sat Jul 14 14:00:43 EDT 2018

CROSSREFS

Cf. A000081, A000837, A001597, A004111, A007097, A007916, A061775, A276625, A277098, A301700, A303431, A316793, A316795, A316796.

#4 by Gus Wiseman at Sat Jul 14 13:55:25 EDT 2018

CROSSREFS

Cf. A000081, A000837 aper, , A001597, A004111, A007097, A007916, A061775, A276625, A277098, 301700, A301700, A303431, A316793, A316795, A316796.

#3 by Gus Wiseman at Sat Jul 14 13:54:58 EDT 2018

CROSSREFS

Cf. A000081, A000837 aper, A001597, A004111, A007097, A007916, A061775, A276625, A277098, 301700, A303431, A316793, A316795, A316796.

#2 by Gus Wiseman at Sat Jul 14 13:42:25 EDT 2018

NAME

allocated for Gus WisemanMatula-Goebel numbers of aperiodic rooted trees with locally distinct multiplicities.

DATA

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

OFFSET

1,2

COMMENTS

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, A000837 aper, A001597, A004111, A007097, A007916, A061775, A276625, A277098, 301700, A303431, A316793.

KEYWORD

allocated

nonn

AUTHOR

Gus Wiseman, Jul 14 2018

STATUS

approved

editing