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A302776 a(1) = 1; for n>1, a(n) = n/(largest Fermi-Dirac factor of n).

%I A302776 #15 Nov 26 2020 03:19:09
%S A302776 1,1,1,1,1,2,1,2,1,2,1,3,1,2,3,1,1,2,1,4,3,2,1,6,1,2,3,4,1,6,1,2,3,2,
%T A302776 5,4,1,2,3,8,1,6,1,4,5,2,1,3,1,2,3,4,1,6,5,8,3,2,1,12,1,2,7,4,5,6,1,4,
%U A302776 3,10,1,8,1,2,3,4,7,6,1,5,1,2,1,12,5,2,3,8,1,10,7,4,3,2,5,6,1,2,9,4,1,6,1,8,15
%N A302776 a(1) = 1; for n>1, a(n) = n/(largest Fermi-Dirac factor of n).
%C A302776 For n > 1, a(n) = the smallest positive number d such that n/d is a "Fermi-Dirac prime", a term of A050376.
%H A302776 Antti Karttunen, <a href="/A302776/b302776.txt">Table of n, a(n) for n = 1..65537</a>
%F A302776 a(n) = n / A223491(n).
%F A302776 a(n) = A302023(A052126(A302024(n))).
%t A302776 f[p_, e_] := p^(2^Floor[Log2[e]]); a[n_] := n / Max @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 26 2020 *)
%o A302776 (PARI)
%o A302776 A209229(n) = (n && !bitand(n,n-1));
%o A302776 A302777(n) = A209229(isprimepower(n));
%o A302776 A302776(n) = if(1==n,n,fordiv(n, d, if(A302777(n/d), return(d))));
%Y A302776 Cf. A050376, A052331, A223491, A302023, A302024, A302777, A302792.
%Y A302776 Cf. A084400 (gives the positions of 1's).
%Y A302776 Cf. also A052126, A284600.
%K A302776 nonn
%O A302776 1,6
%A A302776 _Antti Karttunen_, Apr 13 2018