A225650 The greatest common divisor of Landau g(n) and n.

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, 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, 3, 2, 1, 60, 1, 2, 21, 8, 65, 66, 1, 4, 3, 70, 1, 72, 1, 2, 15, 76, 77, 78, 1

Offset: 0

Author

Antti Karttunen, May 11 2013

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 0..10000

Crossrefs

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.

Cf. A225640-A225643, A225654.

Programs

Mathematica

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 *)

Scheme

(define (A225650 n) (gcd (A000793 n) n))
;; Scheme-code for A000793 can be found in the Program section of that entry.

Formula

a(n) = gcd(n, A000793(n)).