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A387218 Numbers k such that k = sigma(s(s(s(k)))) where s(k) = sigma(k)-k and sigma = A000203.

%I A387218 #29 Aug 30 2025 21:21:46
%S A387218 44,248,11904,565838,583730,16588800
%N A387218 Numbers k such that k = sigma(s(s(s(k)))) where s(k) = sigma(k)-k and sigma = A000203.
%e A387218 k = 44:
%e A387218 s(44) = sigma(44) - 44 = 84 - 44 = 40,
%e A387218 s(40) = sigma(40) - 40 = 90 - 40 = 50,
%e A387218 s(50) = sigma(50) - 50 = 93 - 50 = 43,
%e A387218 sigma(43) = 44.
%e A387218 k = 248:
%e A387218 s(248) = sigma(248) - 248 = 480 - 248 = 232,
%e A387218 s(232) = sigma(232) - 232 = 450 - 232 = 218,
%e A387218 s(218) = sigma(218) - 218 = 330 - 218 = 112,
%e A387218 sigma(112) = 248.
%e A387218 k = 11904:
%e A387218 s(11904) = sigma(11904) - 11904 = 32640 - 11904 = 20736,
%e A387218 s(20736) = sigma(20736) - 20736 = 61831 - 20736 = 41095,
%e A387218 s(41095) = sigma(41095) - 41095 = 49320 - 41095 = 8225,
%e A387218 sigma(8225) = 11904.
%t A387218 s[k_]:=DivisorSigma[1,k]-k;Select[Range[10^6],DivisorSigma[1,s[s[s[#]]]]==#&] (* _James C. McMahon_, Aug 30 2025 *)
%o A387218 (PARI) isok(k) = my(x=sigma(k)-k); if (x>0, x=sigma(x)-x; if (x>0, x=sigma(x)-x; if (x>0, sigma(x) == k))); \\ _Michel Marcus_, Aug 24 2025
%Y A387218 Cf. A000203 (sigma(n)), A001065 (s(n)).
%Y A387218 Cf. A072868 (sigma(sigma(k)-k) = k).
%K A387218 nonn,more,new
%O A387218 1,1
%A A387218 _Hugo Cuéllar_, Aug 22 2025
%E A387218 a(6) from _Michel Marcus_, Aug 24 2025