A097007 a(n) = index of first appearance of n in A096859.
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
Offset: 1
Keywords
Examples
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.
Links
- Klaus Brockhaus, Table of n, a(n) for n=1..119
Programs
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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 -
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 */
Extensions
Edited, a(27) corrected and a(34) through a(36) added by Klaus Brockhaus, Jul 16 2007
Comments