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A316503
Matula-Goebel numbers of unlabeled rooted identity trees with n nodes in which the branches of any node with more than one branch have empty intersection.
4
1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 29, 30, 31, 33, 41, 47, 55, 58, 62, 66, 78, 79, 82, 93, 94, 101, 109, 110, 113, 123, 127, 130, 137, 141, 143, 145, 155, 158, 165, 174, 179, 186, 195, 202, 205, 211, 218, 226, 246, 254, 257, 271, 274, 282, 286, 290, 293
OFFSET
1,2
EXAMPLE
Sequence of rooted identity trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
6: (o(o))
10: (o((o)))
11: ((((o))))
13: ((o(o)))
15: ((o)((o)))
22: (o(((o))))
26: (o(o(o)))
29: ((o((o))))
30: (o(o)((o)))
31: (((((o)))))
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Or[#==1, And[SquareFreeQ[#], Or[PrimeQ[#], GCD@@primeMS[#]==1], And@@#0/@primeMS[#]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2018
STATUS
approved