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A097008
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a(n) = index of first appearance of n in A096862.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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)).
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LINKS
| Klaus Brockhaus, Table of n, a(n) for n=1..120
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EXAMPLE
| 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.
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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
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PROG
| (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 */
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CROSSREFS
| Cf. A062402, A096862, A096863, A096993, A097007.
Sequence in context: A134694 A121606 A166164 * A051653 A106015 A178316
Adjacent sequences: A097005 A097006 A097007 * A097009 A097010 A097011
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 26 2004
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EXTENSIONS
| 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
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