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A322873 Ordinal transform of A300721, which is Möbius transform of A060681.

%I A322873 #11 Dec 19 2021 11:08:27
%S A322873 1,1,1,2,1,2,1,2,2,3,1,3,1,4,3,4,1,4,1,5,2,5,1,6,2,6,2,3,1,7,1,1,2,7,
%T A322873 2,4,1,8,3,2,1,5,1,3,3,9,1,3,2,8,4,4,1,6,2,5,3,10,1,4,1,11,1,5,3,4,1,
%U A322873 6,2,7,1,6,1,12,2,4,1,7,1,7,4,13,1,8,1,14,2,1,1,5,2,3,3,15,1,8,1,8,2,2,1,9,1,3,4
%N A322873 Ordinal transform of A300721, which is Möbius transform of A060681.
%H A322873 Antti Karttunen, <a href="/A322873/b322873.txt">Table of n, a(n) for n = 1..65537</a>
%t A322873 A060681[n_] := n - n/FactorInteger[n][[1, 1]];
%t A322873 A300721[n_] := Sum[MoebiusMu[n/d] A060681[d], {d, Divisors[n]}];
%t A322873 b[_] = 1;
%t A322873 a[n_] := a[n] = With[{t = A300721[n]}, b[t]++];
%t A322873 a /@ Range[1, 105] (* _Jean-François Alcover_, Dec 19 2021 *)
%o A322873 (PARI)
%o A322873 up_to = 65537;
%o A322873 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 A322873 A060681(n) = if(1==n,0,(n-(n/vecmin(factor(n)[, 1]))));
%o A322873 A300721(n) = sumdiv(n, d, moebius(n/d)*A060681(d));
%o A322873 v322873 = ordinal_transform(vector(up_to,n,A300721(n)));
%o A322873 A322873(n) = v322873[n];
%Y A322873 Cf. A060681, A300721, A081373, A303756, A322871, A322874.
%K A322873 nonn
%O A322873 1,4
%A A322873 _Antti Karttunen_, Dec 29 2018