cp's OEIS Frontend

A097007 a(n) = index of first appearance of n in A096859.

%I A097007 #10 Oct 15 2013 22:32:33
%S A097007 1,3,7,18,34,52,100,422,882,1008,960,912,784,1497,3187,13456,21336,
%T A097007 42682,69696,50176,73191,112896,88452,151828,140736,198876,245028,
%U A097007 187272,252964,207936,229456,447201,1412589,9734400,7757136,7910076
%N A097007 a(n) = index of first appearance of n in A096859.
%C A097007 a(n) = smallest k such that A096860(k) + A095955(k) = n.
%C A097007 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 A097007 Klaus Brockhaus, <a href="/A097007/b097007.txt">Table of n, a(n) for n=1..119</a>
%e A097007 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 A097007 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 A097007 of j under iteration of f(x) is completed at an earlier term, hence a(19) = 69696.
%t A097007 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 A097007 (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 A097007 Cf. A062401, A096859, A096860, A095955, A097008.
%K A097007 nonn
%O A097007 1,2
%A A097007 _Labos Elemer_, Jul 26 2004
%E A097007 Edited, a(27) corrected and a(34) through a(36) added by _Klaus Brockhaus_, Jul 16 2007