A110884 a(n) = limiting ratio of successive terms in the trajectory of 1 under the map m -> n*phi(m).

1, 1, 1, 2, 2, 2, 2, 4, 3, 4, 4, 4, 4, 4, 4, 8, 8, 6, 6, 8, 6, 8, 8, 8, 10, 8, 9, 8, 8, 8, 8, 16, 8, 16, 8, 12, 12, 12, 12, 16, 16, 12, 12, 16, 12, 16, 16, 16, 14, 20, 16, 16, 16, 18, 20, 16, 18, 16, 16, 16, 16, 16, 18, 32, 16, 16, 16, 32, 16, 16, 16, 24, 24, 24, 20, 24, 16, 24, 24, 32, 27

Offset

1,4

Comments

Let c(1)=1 and c(k+1)=n*phi(c(k)). Then c(k+1)/c(k) is a decreasing sequence of integers, so eventually becomes constant. a(n) is the ratio between terms once that becomes constant. (In fact, as soon as a ratio repeats, it remains constant from that point on.)

Links

Table of n, a(n) for n=1..81.

Formula

If p prime, a(p)=a(p-1). If every prime divisor of m divides n, a(n*m)=a(n)*m.

Example

For n=25, the sequence m -> n*phi(m) is 1,25,500,5000,50000,...; the ratios are 25,20,10,10,...; so a(25)=10.

Crossrefs

Cf. A000010.

Sequence in context: A097576 A029250 A341584 * A303637 A155904 A241514

Adjacent sequences: A110881 A110882 A110883 * A110885 A110886 A110887

Keyword

easy,nonn

Author

Franklin T. Adams-Watters, Sep 19 2005

Extensions

Definition revised by N. J. A. Sloane, Mar 12 2016

Status

approved