cp's OEIS Frontend

A319917 Unitary sociable numbers of order six.

%I A319917 #28 Feb 16 2025 08:33:56
%S A319917 698130,698310,698490,712710,712890,713070,341354790,348612390,
%T A319917 391662810,406468314,411838938,519891750,530946330,582129630,
%U A319917 596171970,621549630,717175170,740700270,740700450,743324934,838902150,919121658,1009954170,1343332998
%N A319917 Unitary sociable numbers of order six.
%C A319917 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 A319917 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 A319917 J. O. M. Pedersen, <a href="/A319917/a319917.txt">Order 6 cycles</a>, 2007.
%H A319917 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitarySociableNumbers.html">Unitary Sociable Numbers</a>
%o A319917 (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
%o A319917 isok6(n) = iferr(f(f(f(f(f(f(n)))))) == n, E, 0);
%o A319917 isok3(n) = iferr(f(f(f(n))) == n, E, 0);
%o A319917 isok2(n) = iferr(f(f(n)) == n, E, 0);
%o A319917 isok1(n) = iferr(f(n) == n, E, 0);
%o A319917 isok(n) = isok6(n) && !isok1(n) && !isok2(n) && !isok3(n);
%o A319917 (PARI)
%o A319917 A063919(n) = my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^f[i, 2] + 1) - n
%o A319917 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 A319917 Cf. A063919 (sum of proper unitary divisors).
%Y A319917 Cf. A002827 (unitary perfect), A063991 (unitary amicable).
%Y A319917 Cf. A319902 (order 4), A097024 (order 5), A097030 (order 14).
%K A319917 nonn
%O A319917 1,1
%A A319917 _Michel Marcus_, Oct 01 2018