A097007 - OEIS

%I #10 Oct 15 2013 22:32:33

%S 1,3,7,18,34,52,100,422,882,1008,960,912,784,1497,3187,13456,21336,

%T 42682,69696,50176,73191,112896,88452,151828,140736,198876,245028,

%U 187272,252964,207936,229456,447201,1412589,9734400,7757136,7910076

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

%C a(n) = smallest k such that A096860(k) + A095955(k) = n.

%C 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)).

%H Klaus Brockhaus, <a href="/A097007/b097007.txt">Table of n, a(n) for n=1..119</a>

%e 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.

%e 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

%e of j under iteration of f(x) is completed at an earlier term, hence a(19) = 69696.

%t 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

%o (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 */

%Y Cf. A062401, A096859, A096860, A095955, A097008.

%K nonn

%O 1,2

%A _Labos Elemer_, Jul 26 2004

%E Edited, a(27) corrected and a(34) through a(36) added by _Klaus Brockhaus_, Jul 16 2007