cp's OEIS Frontend

A322874 Ordinal transform of A007431, which is Möbius transform of Euler phi.

%I A322874 #11 Dec 20 2021 14:35:33
%S A322874 1,1,2,3,1,2,1,1,1,3,1,4,1,4,2,2,1,5,1,3,2,6,1,2,1,7,1,3,1,8,1,1,2,9,
%T A322874 2,3,1,10,2,1,1,11,1,3,2,12,1,4,1,13,3,3,1,14,2,1,2,15,1,4,1,16,1,2,1,
%U A322874 17,1,4,2,18,1,2,1,19,3,3,2,20,1,3,2,21,1,4,3,22,3,1,1,23,1,3,2,24,2,3,1,25,3,4,1,26,1,1,5
%N A322874 Ordinal transform of A007431, which is Möbius transform of Euler phi.
%H A322874 Antti Karttunen, <a href="/A322874/b322874.txt">Table of n, a(n) for n = 1..65537</a>
%t A322874 A007431[n_] := Sum[EulerPhi[d] MoebiusMu[n/d], {d, Divisors[n]}];
%t A322874 b[_] = 0;
%t A322874 a[n_] := a[n] = With[{t = A007431[n]}, b[t] = b[t]+1];
%t A322874 Array[a, 105] (* _Jean-François Alcover_, Dec 20 2021 *)
%o A322874 (PARI)
%o A322874 up_to = 65537;
%o A322874 ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o A322874 A007431(n) = sumdiv(n,d,moebius(n/d)*eulerphi(d));
%o A322874 v322874 = ordinal_transform(vector(up_to,n,A007431(n)));
%o A322874 A322874(n) = v322874[n];
%Y A322874 Cf. A007431, A081373, A303756, A322873.
%K A322874 nonn
%O A322874 1,3
%A A322874 _Antti Karttunen_, Dec 29 2018