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A330738 Ordinal transform of A049820, where A049820(n) = n - d(n), with d(n) the number of divisors of n (A000005).

%I A330738 #11 Dec 22 2021 09:25:15
%S A330738 1,2,1,2,1,1,1,1,1,2,1,3,1,1,2,3,1,1,1,1,2,1,1,1,1,2,1,3,1,4,1,1,2,1,
%T A330738 1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,2,1,3,2,1,1,1,1,2,1,1,2,3,1,2,1,1,
%U A330738 2,2,1,1,1,1,2,2,1,3,1,4,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,1,1,1,1,2,1,1,1,1,1
%N A330738 Ordinal transform of A049820, where A049820(n) = n - d(n), with d(n) the number of divisors of n (A000005).
%H A330738 Antti Karttunen, <a href="/A330738/b330738.txt">Table of n, a(n) for n = 1..65537</a>
%t A330738 b[_] = 0;
%t A330738 a[n_] := a[n] = With[{t = n - DivisorSigma[0, n]}, b[t] = b[t]+1];
%t A330738 Array[a, 105] (* _Jean-François Alcover_, Dec 22 2021 *)
%o A330738 (PARI)
%o A330738 up_to = 65537;
%o A330738 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 A330738 A049820(n) = (n-numdiv(n));
%o A330738 v330738 = ordinal_transform(vector(up_to, n, A049820(n)));
%o A330738 A330738(n) = v330738[n];
%Y A330738 Cf. A000005, A049820, A060990, A155043.
%K A330738 nonn
%O A330738 1,2
%A A330738 _Antti Karttunen_, Jan 11 2020