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

1,4

Links

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

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 *)

Prog

(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];

Crossrefs

Cf. A060681, A323075, A323164.

Sequence in context: A360330 A035197 A227872 * A091948 A339443 A369323

Adjacent sequences: A323162 A323163 A323164 * A323166 A323167 A323168

Keyword

nonn

Author

Antti Karttunen, Jan 08 2019

Status

approved