A323165 Ordinal transform of A323075 (and also of A323164).

1, 1, 1, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 4, 1, 5, 1, 3, 4, 5, 1, 2, 5, 4, 2, 6, 1, 6, 1, 2, 2, 6, 2, 3, 1, 7, 4, 8, 1, 7, 1, 3, 2, 3, 1, 9, 2, 5, 3, 5, 1, 10, 3, 4, 6, 8, 1, 4, 1, 3, 3, 4, 2, 7, 1, 5, 2, 7, 1, 2, 1, 11, 6, 8, 2, 12, 1, 2, 5, 9, 1, 4, 3, 5, 2, 6, 1, 4, 2, 4, 5, 13, 3, 6, 1, 6, 4, 7, 1, 9, 1, 3, 2

Offset: 1

Author

Antti Karttunen, Jan 08 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A060681, A323075, A323164.

Programs

Mathematica

f[n_] := n - n/FactorInteger[n][[1, 1]]; (* f is A060681 *)
g[n_] := g[n] = If[n == 1+f[n], n, g[1+f[n]]]; (* g is A323075 *)
b[_] = 0;
a[n_] := a[n] = With[{t = g[n]}, b[t] = b[t]+1];
Array[a, 105] (* Jean-François Alcover, Dec 20 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; };
A060681(n) = (n-if(1==n,n,n/vecmin(factor(n)[,1])));
A323075(n) = { my(nn = 1+A060681(n)); if(nn==n,n,A323075(nn)); };
v323165 = ordinal_transform(vector(up_to,n,A323075(n)));
A323165(n) = v323165[n];