A098115 a(n) is the length of iteration-trajectory when cototient-function[=A051953] is applied to the half of n-th primorial number[=A002110(n)/2].

2, 3, 4, 7, 10, 5, 12, 15, 12, 28, 6, 6, 31, 12, 47, 29, 23, 32, 33, 24, 40, 28, 12, 35, 34, 56, 17, 36, 40, 123, 57, 61, 9, 99, 94, 132, 158

Offset

1,1

Comments

Initial values are here odd numbers. Comparing with the case of primorial-iv [=A098202], the lengths are here significantly smaller. Cause of this is unknown, albeit informally "understood": lack of powers of 2 in lists because parity is invariant during this iteration. See also lists for A098200 and A098201.

Links

Table of n, a(n) for n=1..37.

Formula

a[n]=A053475[A002110(n)/2]

Example

n=7: list={255255,163095,77815,16663,895,183,63,27,9,3,1,0},a[7]=12, while comparable length for 510510 is A098202[7]=43.

Mathematica

g[x_] :=x-EulerPhi[x]; f[x_] :=Length[FixedPointList[g, x]]-1; q[x_] :=Apply[Times, Table[Prime[j], {j, 1, x}]]; t=Table[f[q[w]/2], {w, 1, 37}]

Crossrefs

Cf. A051953, A053475, A002110, A098202, A098200, A098201.

Sequence in context: A256772 A274976 A269729 * A182833 A182832 A082673

Adjacent sequences: A098112 A098113 A098114 * A098116 A098117 A098118

Keyword

nonn

Author

Labos Elemer, Sep 27 2004

Status

approved