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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.)