

A097007


a(n) = index of first appearance of n in A096859.


2



1, 3, 7, 18, 34, 52, 100, 422, 882, 1008, 960, 912, 784, 1497, 3187, 13456, 21336, 42682, 69696, 50176, 73191, 112896, 88452, 151828, 140736, 198876, 245028, 187272, 252964, 207936, 229456, 447201, 1412589, 9734400, 7757136, 7910076
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OFFSET

1,2


COMMENTS

a(n) = smallest k such that A096860(k) + A095955(k) = n.
a(n) = smallest k such that n equals the index of the term that completes the first cycle in the trajectory of k under iteration of f(x) = A062401(x) = phi(sigma(x)).


LINKS

Klaus Brockhaus, Table of n, a(n) for n=1..119


EXAMPLE

The trajectory of 18 under iteration of f(x) is 18, 24, 16, 30, 24, 16, 30, ...; the cycle (24, 16, 30) is completed at the fourth term and for j < 18 the first cycle in trajectory of j under iteration of f(x) is completed at the first, second or third term, hence a(4) = 18.
The trajectory of 69696 under iteration of f(x) is 69696, 163296, 157248, 193536, 247808, 217728, 147456, 324000, 285120, 332640, 331776, 900900, 967680, 991232, 1143072, 2122848, 2201472, 1658880, 1801800, 1658880, 1801800, ...; the cycle (1658880, 1801800) is completed at the 19th term and for j < 69696 the first cycle in trajectory
of j under iteration of f(x) is completed at an earlier term, hence a(19) = 69696.


MATHEMATICA

fs[x_] :=EulerPhi[DivisorSigma[1, x]]; nsf[x_, ho_] :=NestList[fs, x, ho]; luf[x_, ho_] :=Length[Union[nsf[x, ho]]] t=Table[0, {35}]; Do[s=luf[n, 100]; If[s<36&&t[[s]]==0, t[[s]]=n], {n, 1, 1600000}]; t


PROG

(PARI) {v=vector(40); for(n=1, 10000000, k=n; s=Set(k); until(setsearch(s, k=eulerphi(sigma(k))), s=setunion(s, Set(k))); a=#s; if(a<=m&&v[a]==0, v[a]=n)); v} /* Klaus Brockhaus, Jul 16 2007 */


CROSSREFS

Cf. A062401, A096859, A096860, A095955, A097008.
Sequence in context: A331713 A327321 A069143 * A308445 A328653 A011799
Adjacent sequences: A097004 A097005 A097006 * A097008 A097009 A097010


KEYWORD

nonn


AUTHOR

Labos Elemer, Jul 26 2004


EXTENSIONS

Edited, a(27) corrected and a(34) through a(36) added by Klaus Brockhaus, Jul 16 2007


STATUS

approved



