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A322873 Ordinal transform of A300721, which is Möbius transform of A060681. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 1 21:24 EST 2023. Contains 359997 sequences. (Running on oeis4.)