cp's OEIS Frontend

A325660 Number of ones in the q-signature of n.

%I A325660 #5 May 13 2019 08:11:44
%S A325660 0,1,2,0,3,1,1,0,0,2,4,1,2,1,1,0,2,0,1,2,2,3,1,1,0,2,0,1,3,1,5,0,2,2,
%T A325660 3,0,2,1,1,2,3,2,2,3,1,1,2,1,0,0,3,2,1,0,1,1,2,3,3,1,1,4,1,0,2,2,2,2,
%U A325660 1,3,3,0,3,2,0,1,4,1,4,2,0,3,2,2,4,2,2
%N A325660 Number of ones in the q-signature of n.
%C A325660 Every positive integer has a unique q-factorization (encoded by A324924) into factors q(i) = prime(i)/i, i > 0. For example:
%C A325660    11 = q(1) q(2) q(3) q(5)
%C A325660    50 = q(1)^3 q(2)^2 q(3)^2
%C A325660   360 = q(1)^6 q(2)^3 q(3)
%C A325660 Then a(n) is the number of factors of multiplicity one in the q-factorization of n.
%C A325660 Also the number of rooted trees appearing only once in the multiset of terminal subtrees of the rooted tree with Matula-Goebel number n.
%t A325660 difac[n_]:=If[n==1,{},With[{i=PrimePi[FactorInteger[n][[1,1]]]},Sort[Prepend[difac[n*i/Prime[i]],i]]]];
%t A325660 Table[Count[Length/@Split[difac[n]],1],{n,100}]
%Y A325660 Cf. A001694, A055231, A056169, A056239, A112798, A118914, A124010.
%Y A325660 Matula-Goebel numbers: A007097, A061775, A109129, A196050, A317713, A324968.
%Y A325660 q-factorization: A324922, A324923, A324924, A325614, A325661.
%K A325660 nonn
%O A325660 1,3
%A A325660 _Gus Wiseman_, May 13 2019