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Ordinal transform of A060681, where A060681(n) = n - A032742(n).
4

%I #12 Dec 19 2021 11:08:13

%S 1,1,1,2,1,1,1,2,2,1,1,3,1,1,2,1,1,1,1,3,1,1,1,2,1,1,2,2,1,1,1,2,2,1,

%T 2,3,1,1,1,2,1,1,1,3,2,1,1,1,2,1,1,2,1,1,1,3,1,1,1,3,1,1,3,1,2,1,1,2,

%U 2,1,1,2,1,1,1,2,2,1,1,2,1,1,1,4,1,1,2,2,1,1,2,3,1,1,1,1,1,1,3,2,1,1,1,3,2

%N Ordinal transform of A060681, where A060681(n) = n - A032742(n).

%H Antti Karttunen, <a href="/A322871/b322871.txt">Table of n, a(n) for n = 1..65537</a>

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

%t b[_] = 1;

%t a[n_] := a[n] = With[{t = A060681[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 v322871 = ordinal_transform(vector(up_to,n,A060681(n)));

%o A322871(n) = v322871[n];

%Y Cf. A032742, A060681, A081373, A303756, A322870, A322872, A322873, A322874.

%K nonn

%O 1,4

%A _Antti Karttunen_, Dec 29 2018