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A302789 Number of times the largest Fermi-Dirac factor of n is the largest Fermi-Dirac factor for numbers <= n; a(1) = 1.

%I A302789 #13 Dec 18 2021 08:06:36
%S A302789 1,1,1,1,1,2,1,2,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,4,1,2,3,4,1,5,1,2,3,2,
%T A302789 5,4,1,2,3,6,1,6,1,4,5,2,1,3,1,2,3,4,1,6,5,7,3,2,1,7,1,2,7,4,5,6,1,4,
%U A302789 3,8,1,8,1,2,3,4,7,6,1,5,1,2,1,9,5,2,3,8,1,9,7,4,3,2,5,6,1,2,9,4,1,6,1,8,10
%N A302789 Number of times the largest Fermi-Dirac factor of n is the largest Fermi-Dirac factor for numbers <= n; a(1) = 1.
%C A302789 Ordinal transform of A223491, or equally, of A302785.
%H A302789 Antti Karttunen, <a href="/A302789/b302789.txt">Table of n, a(n) for n = 1..65537</a>
%t A302789 f[n_] := Max@Table[{p, e} = pe; p^(2^(Length[IntegerDigits[e, 2]]-1)), {pe, FactorInteger[n]}];
%t A302789 b[_] = 1;
%t A302789 a[n_] := a[n] = With[{t = f[n]}, b[t]++];
%t A302789 Array[a, 105] (* _Jean-François Alcover_, Dec 18 2021 *)
%o A302789 (PARI)
%o A302789 up_to = 65537;
%o A302789 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 A302789 ispow2(n) = (n && !bitand(n, n-1));
%o A302789 A223491(n) = if(1==n,n,fordiv(n, d, if(ispow2(isprimepower(n/d)), return(n/d))));
%o A302789 v302789 = ordinal_transform(vector(up_to,n,A223491(n)));
%o A302789 A302789(n) = v302789[n];
%Y A302789 Cf. A050376, A052331, A223491, A302785, A302788.
%Y A302789 Cf. A084400 (gives the positions of 1's).
%Y A302789 Cf. also A078899.
%K A302789 nonn
%O A302789 1,6
%A A302789 _Antti Karttunen_, Apr 13 2018