cp's OEIS Frontend

A319902 Unitary sociable numbers of order 4.

%I A319902 #33 Feb 16 2025 08:33:56
%S A319902 263820,263940,280380,280500,395730,395910,420570,420750,172459210,
%T A319902 209524210,218628662,218725430,230143790,231439570,246667790,
%U A319902 272130250,384121920,384296640,408233280,408408000
%N A319902 Unitary sociable numbers of order 4.
%C A319902 Is this a duplicate of A098188? - _R. J. Mathar_, Oct 04 2018
%C A319902 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.
%C A319902 From _Hartmut F. W. Hoft_, Aug 23 2023: (Start)
%C A319902 This sequence is A098188 in ascending order.
%C A319902 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)
%H A319902 J. O. M. Pedersen, <a href="http://web.archive.org/web/20130731051700/http://amicable.homepage.dk/knwnu4.htm">Known Unitary Sociable Numbers of order four</a> [Via Internet Archive Wayback-Machine]
%H A319902 J. O. M. Pedersen, <a href="/A319902/a319902.txt">Order 4 cycles</a>, 2007.
%H A319902 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitarySociableNumbers.html">Unitary Sociable Numbers</a>
%t A319902 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 *)
%o A319902 (PARI) f(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) - n;
%o A319902 isok4(n) = iferr(f(f(f(f(n)))) == n, E, 0);
%o A319902 isok2(n) = iferr(f(f(n)) == n, E, 0);
%o A319902 isok1(n) = iferr(f(n) == n, E, 0);
%o A319902 isok(n) = isok4(n) && !isok1(n) && !isok2(n);
%Y A319902 Cf. A063919 (sum of proper unitary divisors).
%Y A319902 Cf. A002827 (unitary perfect), A063991 (unitary amicable).
%Y A319902 Cf. A097024 (order 5), A097030 (order 14).
%Y A319902 Cf. A090615 (least member of sociable quadruples).
%Y A319902 Cf. A098188.
%K A319902 nonn,more
%O A319902 1,1
%A A319902 _Michel Marcus_, Oct 01 2018