A330755 Number of values of k, 1 <= k <= n, with A034684(k) = A034684(n), where A034684 gives the smallest unitary divisor of n that is larger than 1.

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 3, 1, 1, 5, 1, 2, 4, 6, 1, 5, 1, 7, 1, 3, 1, 8, 1, 1, 6, 9, 2, 4, 1, 10, 7, 3, 1, 11, 1, 5, 4, 12, 1, 8, 1, 13, 9, 6, 1, 14, 5, 2, 10, 15, 1, 11, 1, 16, 3, 1, 6, 17, 1, 7, 12, 18, 1, 2, 1, 19, 13, 8, 4, 20, 1, 7, 1, 21, 1, 14, 8, 22, 15, 3, 1, 23, 5, 9, 16, 24, 9, 17, 1, 25, 2, 10, 1, 26, 1, 4, 18

Offset: 1

Author

Antti Karttunen, Dec 30 2019

Keywords

• nonn

Comments

Ordinal transform of A034684.

Links

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

Crossrefs

Cf. A034684, A078898, A303759.

Programs

Mathematica

A034684[n_] := With[{f = FactorInteger[n]}, Min[f[[All, 1]]^f[[All, 2]]]];
Module[{b}, b[_] = 0;
a[n_] := With[{t = A034684[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

PARI

up_to = 65537;
A034684(n) = if(1==n,n,my(f=factor(n)); vecmin(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ After code in A034699
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; };
v330755 = ordinal_transform(vector(up_to, n, A034684(n)));
A330755(n) = v330755[n];