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A223491 Largest Fermi-Dirac factor of n.

%I A223491 #21 Nov 26 2020 03:19:01
%S A223491 1,2,3,4,5,3,7,4,9,5,11,4,13,7,5,16,17,9,19,5,7,11,23,4,25,13,9,7,29,
%T A223491 5,31,16,11,17,7,9,37,19,13,5,41,7,43,11,9,23,47,16,49,25,17,13,53,9,
%U A223491 11,7,19,29,59,5,61,31,9,16,13,11,67,17,23,7,71,9
%N A223491 Largest Fermi-Dirac factor of n.
%C A223491 Greatest Fermi-Dirac factor of n: Largest divisor of n of the form p^(2^k), for some prime p and k >= 0, with a(1) = 1. Thus for n > 1, the largest term of A050376 that divides n. - _Antti Karttunen_, Apr 13 2018
%H A223491 Reinhard Zumkeller, <a href="/A223491/b223491.txt">Table of n, a(n) for n = 1..10000</a>
%H A223491 OEIS Wiki, <a href="/wiki/%22Fermi-Dirac_representation%22_of_n">"Fermi-Dirac representation" of n</a>
%F A223491 a(n) = A213925(n,A064547(n)).
%F A223491 A209229(A100995(a(n))) = 1; A010055(a(n)) = 1.
%F A223491 From _Antti Karttunen_, Apr 13 2018: (Start)
%F A223491 a(1) = 1; for n > 1, a(n) = A050376(A302785(n)).
%F A223491 a(n) = n/A302776(n).
%F A223491 (End)
%t A223491 f[p_, e_] := p^(2^Floor[Log2[e]]); a[n_] := Max @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 26 2020 *)
%o A223491 (Haskell)
%o A223491 a223491 = last . a213925_row
%o A223491 (PARI)
%o A223491 ispow2(n) = (n && !bitand(n,n-1));
%o A223491 A223491(n) = if(1==n,n,fordiv(n, d, if(ispow2(isprimepower(n/d)), return(n/d)))); \\ _Antti Karttunen_, Apr 13 2018
%Y A223491 Cf. A223490, A050376, A034699, A000040 (subsequence), A302776, A302785, A302789 (ordinal transform).
%Y A223491 Cf. also A006530, A034699.
%K A223491 nonn
%O A223491 1,2
%A A223491 _Reinhard Zumkeller_, Mar 20 2013