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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
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
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
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