A383392 Numbers k such that (sigma(k) + sigma(k + sigma(k))) / k is an integer where sigma(k) = A000203(k) is the sum of the divisors of k.

1, 3, 14, 19, 27, 28, 48, 139, 164, 243, 496, 1428, 1440, 3360, 3480, 5932, 8128, 11004, 19683, 25296, 27144, 31756, 35616, 45436, 47520, 51480, 84000, 115506, 218520, 221088, 288288, 290520, 303309, 414528, 445788, 605880, 1019070, 1122432, 2100000, 2136288

Offset: 1

Author

Ctibor O. Zizka, Apr 25 2025

Keywords

• nonn

Examples

			k = 3: (sigma(3) + sigma(3 + sigma(3)))/3 = (4 + 8)/3 = 4.
		

Crossrefs

Cf. A000203, A007691, A246456.

Programs

Mathematica

q[k_] := Module[{s = DivisorSigma[1, k]}, Divisible[s + DivisorSigma[1, k + s], k]]; Select[Range[2200000], q] (* Amiram Eldar, Apr 25 2025 *)

PARI

isok(k) = my(s=sigma(k)); ((s+sigma(k+s)) % k) == 0; \\ Michel Marcus, Apr 25 2025