A318692 Matula-Goebel numbers of series-reduced powerful uniform rooted trees.

1, 4, 8, 16, 32, 49, 64, 128, 196, 256, 343, 361, 512, 1024, 1444, 2048, 2401, 2744, 2809, 4096, 6859, 8192, 11236, 16384, 16807, 17161, 17689, 32768, 38416, 51529, 54872, 65536, 68644, 70756, 96721, 117649, 130321, 131072, 137641, 148877, 206116, 262144

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 series-reduced powerful uniform rooted tree iff either n = 1 or n is a squarefree number, whose prime indices are all Matula-Goebel numbers of series-reduced powerful uniform rooted trees, taken to a power > 1.

Links

Table of n, a(n) for n=1..42.

Example

The sequence of all series-reduced powerful uniform rooted trees together with their Matula-Goebel numbers begins:
    1: o
    4: (oo)
    8: (ooo)
   16: (oooo)
   32: (ooooo)
   49: ((oo)(oo))
   64: (oooooo)
  128: (ooooooo)
  196: (oo(oo)(oo))
  256: (oooooooo)
  343: ((oo)(oo)(oo))
  361: ((ooo)(ooo))
  512: (ooooooooo)

Mathematica

srpowunQ[n_]:=Or[n==1, And[SameQ@@FactorInteger[n][[All, 2]], Min@@FactorInteger[n][[All, 2]]>1, And@@srpowunQ/@PrimePi/@FactorInteger[n][[All, 1]]]];
Select[Range[100000], srpowunQ]

Crossrefs

Cf. A000081, A001694, A061775, A072774, A214577, A291636, A317705, A317707, A317710, A318611, A318612, A318690, A318691.

Sequence in context: A048168 A175341 A317705 * A291441 A331967 A301147

Adjacent sequences: A318689 A318690 A318691 * A318693 A318694 A318695

Keyword

nonn

Author

Gus Wiseman, Aug 31 2018

Status

approved