A097008 a(n) = index of first appearance of n in A096862.

1, 2, 5, 11, 19, 43, 53, 101, 1297, 883, 1009, 1037, 1051, 985, 2391, 12101, 13457, 21887, 42683, 69697, 50177, 115601, 113669, 88897, 156817, 184477, 247487, 245029, 187273, 287543, 211031, 287093, 1001447, 5398093, 9741229, 7757137

Offset: 1

Author

Labos Elemer, Jul 26 2004

Keywords

• nonn

Comments

a(n) = smallest k such that A096863(k) + A096993(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) = A062402(x) = sigma(phi(x)).

Examples

			The trajectory of 19 under iteration of f(x) is 19, 39, 60, 31, 72, 60, 31, 72, ...; the cycle (60, 31, 72) is completed at the fifth term and for j < 19 the first cycle in trajectory of j under iteration of f(x) is completed at the first, second, third or fourth term, hence a(5) = 19.
The trajectory of 247487 under iteration of f(x) is 247487, 787200, 507873, 1282842, 1395372, 1476096, 1572096, 1089403, 3669120, 2621120, 4464096, 3963960, 2946240, 2538280, 3265416, 2877420, 1965840, 2227680, 1310680, 1591200, 1277874, 1307124, 1110488, 2010960, 1488032, 1981496, 2239920, 1965840, ...; the cycle (1965840, 2227680,
..., 2239920) is completed at the 27th term and for j < 247487 the first cycle in trajectory of j under iteration of f(x) is completed at an earlier term, hence a(27) = 247487.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n=1..120

Crossrefs

Cf. A062402, A096862, A096863, A096993, A097007.

Programs

Mathematica

sf[x_] :=DivisorSigma[1, EulerPhi[x]]; nsf[x_, ho_] :=NestList[sf, 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, 1500000}];t

PARI

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

Extensions

Edited, a(27) and a(33) corrected and a(34) through a(36) added by Klaus Brockhaus, Jul 16 2007