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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 11 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000005, A049820, A060990, A155043.

Programs

Mathematica

b[_] = 0;
a[n_] := a[n] = With[{t = n - DivisorSigma[0, n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 22 2021 *)

PARI

up_to = 65537;
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; };
A049820(n) = (n-numdiv(n));
v330738 = ordinal_transform(vector(up_to, n, A049820(n)));
A330738(n) = v330738[n];