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 A097007 a(n) = index of first appearance of n in A096859. 2
 1, 3, 7, 18, 34, 52, 100, 422, 882, 1008, 960, 912, 784, 1497, 3187, 13456, 21336, 42682, 69696, 50176, 73191, 112896, 88452, 151828, 140736, 198876, 245028, 187272, 252964, 207936, 229456, 447201, 1412589, 9734400, 7757136, 7910076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = smallest k such that A096860(k) + A095955(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) = A062401(x) = phi(sigma(x)). LINKS Klaus Brockhaus, Table of n, a(n) for n=1..119 EXAMPLE 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. 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 of j under iteration of f(x) is completed at an earlier term, hence a(19) = 69696. MATHEMATICA 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 PROG (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 */ CROSSREFS Cf. A062401, A096859, A096860, A095955, A097008. Sequence in context: A331713 A327321 A069143 * A308445 A328653 A011799 Adjacent sequences:  A097004 A097005 A097006 * A097008 A097009 A097010 KEYWORD nonn AUTHOR Labos Elemer, Jul 26 2004 EXTENSIONS Edited, a(27) corrected and a(34) through a(36) added by Klaus Brockhaus, Jul 16 2007 STATUS approved

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Last modified October 27 13:45 EDT 2021. Contains 348276 sequences. (Running on oeis4.)