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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.
3
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
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2019
STATUS
approved