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A318612 Matula-Goebel numbers of powerful rooted trees. 6
1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 25, 27, 31, 32, 36, 49, 53, 59, 64, 67, 72, 81, 83, 97, 100, 103, 108, 121, 125, 127, 128, 131, 144, 151, 196, 200, 216, 225, 227, 241, 243, 256, 277, 288, 289, 311, 324, 331, 343, 359, 361, 392, 400, 419, 431, 432 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A prime index of n is a number m such that prime(m) divides n. A positive integer n is a Matula-Goebel number of a powerful rooted tree iff either n = 1 or n is a prime number whose prime index is a Matula-Goebel number of a powerful rooted tree or n is a powerful number (meaning its prime multiplicities are all greater than 1) whose prime indices are all Matula-Goebel numbers of powerful rooted trees.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

The sequence of all powerful rooted trees together with their Matula-Goebel numbers begins:

   1: o

   2: (o)

   3: ((o))

   4: (oo)

   5: (((o)))

   7: ((oo))

   8: (ooo)

   9: ((o)(o))

  11: ((((o))))

  16: (oooo)

  17: (((oo)))

  19: ((ooo))

  23: (((o)(o)))

  25: (((o))((o)))

  27: ((o)(o)(o))

  31: (((((o)))))

MATHEMATICA

powgoQ[n_]:=Or[n==1, If[PrimeQ[n], powgoQ[PrimePi[n]], And[Min@@FactorInteger[n][[All, 2]]>1, And@@powgoQ/@PrimePi/@FactorInteger[n][[All, 1]]]]];

Select[Range[1000], powgoQ]

CROSSREFS

Complement of A317719.

Cf. A000081, A001694, A061775, A111299, A214577, A276625, A303431, A317102, A317705, A317707.

Sequence in context: A316468 A099627 A184155 * A318690 A302498 A243497

Adjacent sequences:  A318609 A318610 A318611 * A318613 A318614 A318615

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 30 2018

STATUS

approved

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Last modified February 19 20:17 EST 2019. Contains 320328 sequences. (Running on oeis4.)