A322871 Ordinal transform of A060681, where A060681(n) = n - A032742(n).

1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 2

Offset: 1

Author

Antti Karttunen, Dec 29 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A032742, A060681, A081373, A303756, A322870, A322872, A322873, A322874.

Programs

Mathematica

A060681[n_] := n - n/FactorInteger[n][[1, 1]];
b[_] = 1;
a[n_] := a[n] = With[{t = A060681[n]}, b[t]++];
a /@ Range[1, 105] (* Jean-François Alcover, Dec 19 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) = if(1==n,0,(n-(n/vecmin(factor(n)[, 1]))));
v322871 = ordinal_transform(vector(up_to,n,A060681(n)));
A322871(n) = v322871[n];