A330752 Number of values of k, 1 <= k <= n, with A328478(k) = A328478(n), where A328478(n) gives the remainder when all maximal primorial divisors of n (from the largest to smallest) have been divided out.

1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 1, 6, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 8, 1, 2, 1, 3, 1, 9, 1, 10, 1, 2, 1, 11, 1, 2, 1, 4, 1, 4, 1, 3, 1, 2, 1, 12, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 13, 1, 2, 1, 14, 1, 4, 1, 3, 1, 2, 1, 15, 1, 2, 1, 3, 1, 4, 1, 5, 1, 2, 1, 6, 1, 2, 1, 5, 1, 3, 1, 3, 1, 2, 1, 16, 1, 2, 1, 3, 1, 4, 1, 5, 1

Offset: 1

Author

Antti Karttunen, Dec 30 2019

Keywords

• nonn

Comments

Ordinal transform of A328478.

Links

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

Crossrefs

Cf. A111701, A328478, A330751.

Programs

Mathematica

A111701[n_] := A111701[n] = Block[{m = n, k = 1}, While[IntegerQ[m/Prime[k]], m = m/Prime[k]; k++]; m];
A328478[n_] := A328478[n] = If[A111701[n] == n, n, A328478[A111701[n]]];
Module[{b}, b[_] = 0;
a[n_] := With[{t = A328478[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 11 2022, after Robert G. Wilson v in A111701 *)

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; };
A111701(n) = forprime(p=2, , if(n%p, return(n), n /= p));
A328478(n) = { my(u=A111701(n)); if(u==n, return(n), return(A328478(u))); };
v330752 = ordinal_transform(vector(up_to, n, A328478(n)));
A330752(n) = v330752[n];