A302789 - OEIS

%I #13 Dec 18 2021 08:06:36

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

%C Ordinal transform of A223491, or equally, of A302785.

%H Antti Karttunen, <a href="/A302789/b302789.txt">Table of n, a(n) for n = 1..65537</a>

%t f[n_] := Max@Table[{p, e} = pe; p^(2^(Length[IntegerDigits[e, 2]]-1)), {pe, FactorInteger[n]}];

%t b[_] = 1;

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

%t Array[a, 105] (* _Jean-François Alcover_, Dec 18 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 ispow2(n) = (n && !bitand(n, n-1));

%o A223491(n) = if(1==n,n,fordiv(n, d, if(ispow2(isprimepower(n/d)), return(n/d))));

%o v302789 = ordinal_transform(vector(up_to,n,A223491(n)));

%o A302789(n) = v302789[n];

%Y Cf. A050376, A052331, A223491, A302785, A302788.

%Y Cf. A084400 (gives the positions of 1's).

%Y Cf. also A078899.

%K nonn

%O 1,6

%A _Antti Karttunen_, Apr 13 2018