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

0,3

Links

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

Formula

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

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 *)

Prog

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

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.

Sequence in context: A101174 A050144 A124406 * A340087 A239223 A143771

Adjacent sequences: A225647 A225648 A225649 * A225651 A225652 A225653

Keyword

nonn

Author

Antti Karttunen, May 11 2013

Status

approved