A306202 - OEIS

%I #8 Jun 25 2021 23:41:26

%S 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,

%T 31,32,33,34,35,37,38,39,40,41,42,43,44,47,48,51,52,53,55,56,57,58,59,

%U 60,62,64,65,66,67,68,70,71,73,74,76,77,78,79,80,82,84,85

%N Matula-Goebel numbers of rooted semi-identity trees.

%C 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.

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>

%e The sequence of all unlabeled rooted semi-identity trees together with their Matula-Goebel numbers begins:

%e    1: o

%e    2: (o)

%e    3: ((o))

%e    4: (oo)

%e    5: (((o)))

%e    6: (o(o))

%e    7: ((oo))

%e    8: (ooo)

%e   10: (o((o)))

%e   11: ((((o))))

%e   12: (oo(o))

%e   13: ((o(o)))

%e   14: (o(oo))

%e   15: ((o)((o)))

%e   16: (oooo)

%e   17: (((oo)))

%e   19: ((ooo))

%e   20: (oo((o)))

%e   21: ((o)(oo))

%e   22: (o(((o))))

%e   24: (ooo(o))

%e   26: (o(o(o)))

%e   28: (oo(oo))

%e   29: ((o((o))))

%e   30: (o(o)((o)))

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t psidQ[n_]:=And[UnsameQ@@DeleteCases[primeMS[n],1],And@@psidQ/@primeMS[n]];

%t Select[Range[100],psidQ]

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Jan 29 2019