A387218 Numbers k such that k = sigma(s(s(s(k)))) where s(k) = sigma(k)-k and sigma = A000203.
44, 248, 11904, 565838, 583730, 16588800
Offset: 1
Examples
k = 44: s(44) = sigma(44) - 44 = 84 - 44 = 40, s(40) = sigma(40) - 40 = 90 - 40 = 50, s(50) = sigma(50) - 50 = 93 - 50 = 43, sigma(43) = 44. k = 248: s(248) = sigma(248) - 248 = 480 - 248 = 232, s(232) = sigma(232) - 232 = 450 - 232 = 218, s(218) = sigma(218) - 218 = 330 - 218 = 112, sigma(112) = 248. k = 11904: s(11904) = sigma(11904) - 11904 = 32640 - 11904 = 20736, s(20736) = sigma(20736) - 20736 = 61831 - 20736 = 41095, s(41095) = sigma(41095) - 41095 = 49320 - 41095 = 8225, sigma(8225) = 11904.
Programs
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Mathematica
s[k_]:=DivisorSigma[1,k]-k;Select[Range[10^6],DivisorSigma[1,s[s[s[#]]]]==#&] (* James C. McMahon, Aug 30 2025 *)
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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
Extensions
a(6) from Michel Marcus, Aug 24 2025