A322873 Ordinal transform of A300721, which is Möbius transform of A060681.

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

Offset

1,4

Links

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

Mathematica

A060681[n_] := n - n/FactorInteger[n][[1, 1]];
A300721[n_] := Sum[MoebiusMu[n/d] A060681[d], {d, Divisors[n]}];
b[_] = 1;
a[n_] := a[n] = With[{t = A300721[n]}, b[t]++];
a /@ Range[1, 105] (* Jean-François Alcover, Dec 19 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) = if(1==n, 0, (n-(n/vecmin(factor(n)[, 1]))));
A300721(n) = sumdiv(n, d, moebius(n/d)*A060681(d));
v322873 = ordinal_transform(vector(up_to, n, A300721(n)));
A322873(n) = v322873[n];

Crossrefs

Cf. A060681, A300721, A081373, A303756, A322871, A322874.

Sequence in context: A291598 A287820 A191373 * A332897 A349552 A026904

Adjacent sequences: A322870 A322871 A322872 * A322874 A322875 A322876

Keyword

nonn

Author

Antti Karttunen, Dec 29 2018

Status

approved