

A098115


a(n) is the length of iterationtrajectory when cototientfunction[=A051953] is applied to the half of nth primorial number[=A002110(n)/2].


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Initial values are here odd numbers. Comparing with the case of primorialiv [=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_] :=xEulerPhi[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



