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%I #21 Sep 09 2017 19:36:12
%S 1,1,2,3,4,1,6,1,1,1,10,1,12,1,14,15,4,1,6,1,20,21,2,1,24,5,2,1,14,1,
%T 30,1,4,3,2,35,36,1,2,39,40,1,42,1,44,15,2,1,24,7,10,3,52,1,18,55,56,
%U 3,2,1,60,1,2,21,8,65,66,1,4,3,70,1,72,1,2,15,76,77,78,1
%N The greatest common divisor of Landau g(n) and n.
%H R. J. Mathar, <a href="/A225650/b225650.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = gcd(n, A000793(n)).
%t b[n_, i_] := b[n, i] = Module[{p}, p = If[i < 1, 1, Prime[i]]; If[n == 0 || i < 1, 1, Max[b[n, i - 1], Table[p^j*b[n - p^j, i - 1], {j, 1, Log[p, n] // Floor}]]]]; g[n_] := b[n, If[n < 8, 3, PrimePi[Ceiling[1.328*Sqrt[n* Log[n] // Floor]]]]]; a[n_] := GCD[n, g[n]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Mar 02 2016, after _Alois P. Heinz_ *)
%o (Scheme): (define (A225650 n) (gcd (A000793 n) n))
%o ;; Scheme-code for A000793 can be found in the Program section of that entry.
%Y A225648 gives the position of ones, and likewise A225651 gives the positions of fixed points, that is, a(A225651(n)) = A225651(n) for all n.
%Y Cf. A225640-A225643, A225654.
%K nonn
%O 0,3
%A _Antti Karttunen_, May 11 2013