A320230 - OEIS

%I #8 Apr 05 2021 03:55:12

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,22,23,24,25,26,27,28,

%T 29,31,32,34,36,37,38,40,41,43,44,46,48,49,50,52,53,54,56,58,59,61,62,

%U 64,67,68,71,72,74,76,79,80,81,82,83,86,88,89,92,96,97

%N Matula-Goebel numbers of rooted trees in which the non-leaf branches directly under any given node are all equal.

%C A number is in the sequence iff it belongs to A070776 and its prime indices already belong to the sequence. A prime index of n is a number m such that prime(m) divides n.

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

%t smakQ[n_]:=And[SameQ@@DeleteCases[primeMS[n],1],And@@smakQ/@DeleteCases[primeMS[n],1]];Select[Range[100],smakQ[#]&]

%o (PARI) is(n) = while((n>>=valuation(n,2)) > 1, isprimepower(n,&n) || return(0); n=primepi(n)); 1; \\ _Kevin Ryde_, Apr 04 2021

%Y Cf. A002541, A070776, A214577, A294336, A317710, A320222, A320226.

%K nonn

%O 1,2

%A _Gus Wiseman_, Oct 08 2018