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A097007
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a(n) = index of first appearance of n in A096859.
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2
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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
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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) = A062401(x) = phi(sigma(x)).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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
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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=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 */
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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) 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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