A322873 - OEIS

%I #11 Dec 19 2021 11:08:27

%S 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,

%T 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,

%U 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

%N Ordinal transform of A300721, which is Möbius transform of A060681.

%H Antti Karttunen, <a href="/A322873/b322873.txt">Table of n, a(n) for n = 1..65537</a>

%t A060681[n_] := n - n/FactorInteger[n][[1, 1]];

%t A300721[n_] := Sum[MoebiusMu[n/d] A060681[d], {d, Divisors[n]}];

%t b[_] = 1;

%t a[n_] := a[n] = With[{t = A300721[n]}, b[t]++];

%t a /@ Range[1, 105] (* _Jean-François Alcover_, Dec 19 2021 *)

%o (PARI)

%o up_to = 65537;

%o 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; };

%o A060681(n) = if(1==n,0,(n-(n/vecmin(factor(n)[, 1]))));

%o A300721(n) = sumdiv(n, d, moebius(n/d)*A060681(d));

%o v322873 = ordinal_transform(vector(up_to,n,A300721(n)));

%o A322873(n) = v322873[n];

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 29 2018