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

Author

Gus Wiseman, Aug 31 2018

Keywords

• nonn

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.

Examples

			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)
		

Crossrefs

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

Programs

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]