cp's OEIS Frontend

A325611 Number of nodes in the rooted tree with Matula-Goebel number 2^n - 1.

%I A325611 #5 May 13 2019 01:10:01
%S A325611 1,3,4,6,6,8,7,10,10,12,12,15,12,14,16,18,14,20,16,23,20,22,22,25,25,
%T A325611 24,23,29,26,30,27,31,33,28,32,38,36,31,36,40,37,38,33,43,44,42,39,48,
%U A325611 39,49,45,48,43,49,49,53,47,54,47,61
%N A325611 Number of nodes in the rooted tree with Matula-Goebel number 2^n - 1.
%C A325611 Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
%C A325611    11 = q(1) q(2) q(3) q(5)
%C A325611    50 = q(1)^3 q(2)^2 q(3)^2
%C A325611   360 = q(1)^6 q(2)^3 q(3)
%C A325611 Then a(n) is one plus the number of factors (counted with multiplicity) in the q-factorization of 2^n - 1.
%e A325611 The rooted tree with Matula-Goebel number 2047 = 2^11 - 1 is (((o)(o))(ooo(o))), which has 12 nodes (o's plus brackets), so a(11) = 12.
%t A325611 mgwt[n_]:=If[n==1,1,1+Total[Cases[FactorInteger[n],{p_,k_}:>mgwt[PrimePi[p]]*k]]];
%t A325611 Table[mgwt[2^n-1],{n,30}]
%Y A325611 Cf. A001222, A001221, A056239, A112798.
%Y A325611 Matula-Goebel numbers: A007097, A061775, A109082, A109129, A196050, A317713.
%Y A325611 Mersenne numbers: A046051, A046800, A059305, A325610, A325612, A325625.
%K A325611 nonn
%O A325611 1,2
%A A325611 _Gus Wiseman_, May 12 2019