1,2

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)).

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

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.

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 */

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

Sequence in context: A134694 A121606 A166164 this_sequence A051653 A106015 A093871

Adjacent sequences: A097005 A097006 A097007 this_sequence A097009 A097010 A097011

nonn

Labos E. (labos(AT)ana.sote.hu), Jul 26 2004

Edited, a(27) and a(33) corrected and a(34) through a(36) added by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 16 2007