A306202 Matula-Goebel numbers of rooted semi-identity trees.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 70, 71, 73, 74, 76, 77, 78, 79, 80, 82, 84, 85

Offset: 1

Author

Gus Wiseman, Jan 29 2019

Keywords

• nonn

Comments

Definition: A positive integer belongs to the sequence iff its prime indices greater than 1 are distinct and already belong to the sequence. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			The sequence of all unlabeled rooted semi-identity trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   6: (o(o))
   7: ((oo))
   8: (ooo)
  10: (o((o)))
  11: ((((o))))
  12: (oo(o))
  13: ((o(o)))
  14: (o(oo))
  15: ((o)((o)))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  20: (oo((o)))
  21: ((o)(oo))
  22: (o(((o))))
  24: (ooo(o))
  26: (o(o(o)))
  28: (oo(oo))
  29: ((o((o))))
  30: (o(o)((o)))
		

Links

• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Cf. A000081, A004111, A007097, A276625, A277098, A306200, A306201, A316467.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
psidQ[n_]:=And[UnsameQ@@DeleteCases[primeMS[n],1],And@@psidQ/@primeMS[n]];
Select[Range[100],psidQ]