A324845 Matula-Goebel numbers of rooted trees where the branches of no non-leaf branch of any terminal subtree form a submultiset of the branches of the same subtree.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 14, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 34, 35, 38, 40, 43, 44, 46, 49, 50, 51, 53, 57, 58, 59, 62, 63, 64, 67, 68, 69, 70, 71, 73, 76, 77, 79, 80, 81, 83, 85, 86, 87, 88, 92, 93, 95, 97, 98, 99, 100, 103, 106

Offset

1,2

Links

Table of n, a(n) for n=1..66.

Gus Wiseman, The sequence of rooted trees whose Matula-Goebel numbers belong to A324845.

Example

The sequence of terms together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   7: ((oo))
   8: (ooo)
   9: ((o)(o))
  10: (o((o)))
  11: ((((o))))
  14: (o(oo))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  20: (oo((o)))
  21: ((o)(oo))
  22: (o(((o))))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))

Mathematica

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

Crossrefs

Cf. A000081, A007097, A290822, A306844, A318186.

Cf. A324694, A324738, A324744, A324749, A324754, A324759, A324765, A324768, A324838, A324842, A324844, A324846, A324847, A324849.

Sequence in context: A032894 A032853 A023748 * A107686 A004743 A333764

Adjacent sequences: A324842 A324843 A324844 * A324846 A324847 A324848

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved