A316521 - OEIS

%I #4 Jul 06 2018 17:05:25

%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29,30,31,

%T 32,33,34,35,38,39,41,42,43,46,47,49,51,53,55,57,58,59,62,64,65,66,67,

%U 69,70,73,77,78,79,81,82,83,85,86,87,91,93,94,95,97,101

%N Matula-Goebel numbers of rooted trees where all terminal rooted subtrees are either constant or strict.

%C The following are equivalent.

%C   1. n is in the sequence.

%C   2. prime(n) is in the sequence.

%C   3. n is a product of prime numbers that are already in the sequence and that are either all equal or all different.

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

%t go[n_]:=And[Or[SameQ@@primeMS[n],UnsameQ@@primeMS[n]],And@@go/@primeMS[n]]

%t Select[Range[100],go]

%Y Cf. A000081, A000961, A003238, A004111, A005117, A007097, A072774, A214577, A276625, A277098.

%K nonn

%O 1,2

%A _Gus Wiseman_, Jul 05 2018