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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
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OFFSET
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1,2
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COMMENTS
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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
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EXAMPLE
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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
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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
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(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
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited, a(27) and a(33) corrected and a(34) through a(36) added by Klaus Brockhaus, Jul 16 2007
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STATUS
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approved
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