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

1,6

Comments

Ordinal transform of A034684.

Links

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

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 *)

Prog

(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];

Crossrefs

Cf. A034684, A078898, A303759.

Sequence in context: A372572 A120454 A321648 * A316431 A319567 A076511

Adjacent sequences: A330752 A330753 A330754 * A330756 A330757 A330758

Keyword

nonn

Author

Antti Karttunen, Dec 30 2019

Status

approved