A330752 - OEIS

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

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OFFSET

1,2

COMMENTS

Ordinal transform of A328478.

LINKS

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

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 *)

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; };

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];

CROSSREFS

Cf. A111701, A328478, A330751.

Sequence in context: A085343 A049077 A180184 * A222266 A077609 A077610

Adjacent sequences: A330749 A330750 A330751 * A330753 A330754 A330755

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 30 2019

STATUS

approved