%I #27 Aug 31 2021 04:37:08

%S 698130,698310,698490,712710,712890,713070,341354790,348612390,

%T 391662810,406468314,411838938,519891750,530946330,582129630,

%U 596171970,621549630,717175170,740700270,740700450,743324934,838902150,919121658,1009954170,1343332998

%N Unitary sociable numbers of order six.

%C Note that the first 6 terms and the next 6 terms form two sociable groups. But then the next 12 terms belong to two distinct sociable groups.

%H J. O. M. Pedersen, <a href="http://web.archive.org/web/20130731050921/http://amicable.homepage.dk/knwnux.htm">Known Unitary Sociable Numbers of order different from four</a> [Via Internet Archive Wayback-Machine]

%H J. O. M. Pedersen, <a href="/A319917/a319917.txt">Order 6 cycles</a>, 2007.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitarySociableNumbers.html">Unitary Sociable Numbers</a>

%o (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;

%o isok6(n) = iferr(f(f(f(f(f(f(n)))))) == n, E, 0);

%o isok3(n) = iferr(f(f(f(n))) == n, E, 0);

%o isok2(n) = iferr(f(f(n)) == n, E, 0);

%o isok1(n) = iferr(f(n) == n, E, 0);

%o isok(n) = isok6(n) && !isok1(n) && !isok2(n) && !isok3(n);

%o (PARI)

%o A063919(n) = my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1) - n

%o is(n) = my(c = n); for(i = 1, 5, c = A063919(c); if(c == 1 || c == n, return(0))); c = A063919(c); c == n \\ _David A. Corneth_, Oct 01 2018

%Y Cf. A063919 (sum of proper unitary divisors).

%Y Cf. A002827 (unitary perfect), A063991 (unitary amicable).

%Y Cf. A319902 (order 4), A097024 (order 5), A097030 (order 14).

%K nonn

%O 1,1

%A _Michel Marcus_, Oct 01 2018