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

Author

Hugo Cuéllar, Aug 22 2025

Keywords

• nonn
• more
• new

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.
		

Crossrefs

Cf. A000203 (sigma(n)), A001065 (s(n)).

Cf. A072868 (sigma(sigma(k)-k) = k).

Programs

Mathematica

s[k_]:=DivisorSigma[1,k]-k;Select[Range[10^6],DivisorSigma[1,s[s[s[#]]]]==#&] (* James C. McMahon, Aug 30 2025 *)

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