A098188 -id:A098188 - cp's OEIS frontend

A319902 Unitary sociable numbers of order 4.

263820, 263940, 280380, 280500, 395730, 395910, 420570, 420750, 172459210, 209524210, 218628662, 218725430, 230143790, 231439570, 246667790, 272130250, 384121920, 384296640, 408233280, 408408000

Offset: 1

Michel Marcus, Oct 01 2018

Is this a duplicate of A098188? - R. J. Mathar, Oct 04 2018
Note that the first 4 terms and the next 4 terms form two sociable groups. But then the next 8 terms belong to two distinct sociable groups, whereas in A098188 the integers are grouped by cycle.
From Hartmut F. W. Hoft, Aug 23 2023: (Start)
This sequence is A098188 in ascending order.
Among the 19 4-cycles listed in the link by J. O. M. Pedersen only four of the 6 possible patterns of relative sizes of the numbers in a cycle are realized. (End)

J. O. M. Pedersen, Known Unitary Sociable Numbers of order four [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Order 4 cycles, 2007.
Eric Weisstein's World of Mathematics, Unitary Sociable Numbers

Cf. A063919 (sum of proper unitary divisors).
Cf. A002827 (unitary perfect), A063991 (unitary amicable).
Cf. A097024 (order 5), A097030 (order 14).
Cf. A090615 (least member of sociable quadruples).
Cf. A098188.

f[n_] := f[n] = Module[{s = 0}, s = Total[Select[Divisors[n], GCD[#, n/#] == 1 &]]; Return[s - n]]; isok1[n_] := isok1[n] = Quiet[Check[f[n] == n, 0]]; isok2[n_] := isok2[n] = Quiet[Check[f[f[n]] == n, 0]]; isok4[n_] := isok4[n] = Quiet[Check[f[f[f[f[n]]]] == n, 0]]; isok[n_] := isok[n] = isok4[n] && Not[isok1[n]] && Not[isok2[n]]; Monitor[Position[Table[isok[n], {n, 1, 408408000}], True], n] (* Robert P. P. McKone, Aug 24 2023 *)

f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
isok4(n) = iferr(f(f(f(f(n)))) == n, E, 0);
isok2(n) = iferr(f(f(n)) == n, E, 0);
isok1(n) = iferr(f(n) == n, E, 0);
isok(n) = isok4(n) && !isok1(n) && !isok2(n);

A098187 Initial seeds x which will enter a cycle of length 4 under the iteration of x -> A063919(x), the sum of proper unitary divisors.

Original entry on oeis.org

81570, 114270, 137046, 169998, 177906, 182082, 182094, 185190, 194574, 194586, 201642, 203442, 204420, 204540, 212466, 212874, 213870, 219306, 219318, 230874, 231438, 231834, 231846, 232626, 237678, 238134, 242634, 258882, 259338, 259350

Offset: 1

Labos Elemer, Sep 02 2004

nonn

The sequence is the attractor-basin of set of {C4} cycles belonging to this iteration.

The {C4} attractor-set is displayed separately in A098188.

			81570 is in the sequence because its track under the iterated map is 81570, 114270, 182082, 182094, 232626, 237678, 305682, 352878, 360978, 403662, 420738, [420750, 395730, 395910, 420570], 420750.., where the cycle is indicated by brackets. The 4 recurrent terms appear after 11 transients for this case.

Cf. A098185, A098186, A002827, A097024, A097030.

cp's OEIS Frontend

A319902 Unitary sociable numbers of order 4.

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