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

1,2

Links

Table of n, a(n) for n=1..40.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A007691, A246456.

Sequence in context: A121459 A121226 A063633 * A108933 A271384 A015639

Adjacent sequences: A383389 A383390 A383391 * A383393 A383394 A383395

Keyword

nonn

Author

Ctibor O. Zizka, Apr 25 2025

Status

approved