A057852 Numbers k such that k | sigma_2(k) + sigma_1(k) + sigma_0(k).

1, 2, 6, 8, 27, 30, 42, 60, 130, 611, 837, 1196, 7524, 10640, 14160, 16836, 43268, 59856, 83121, 90960, 317424, 688704, 718643, 769101, 4714800, 11339016, 15819208, 25553726, 37282080, 53056400, 97012042, 190740298, 403501008, 2047926288, 2269180408, 2513120880, 2549752080

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Mathematica

Do[ If[ Mod[ DivisorSigma[ 2, n] + DivisorSigma[ 1, n] + DivisorSigma[ 0, n], n] == 0, Print[n]], {n, 1, 10^7}]
With[{c=Total[Table[DivisorSigma[x, #], {x, 0, 2}]]}, Select[Range[800000], Mod[c, #]==0&]] (* Harvey P. Dale, May 23 2023 *)

Prog

(PARI) isok(k) = my(f = factor(k)); !(sum(i = 0, 2, sigma(f, i)) % k); \\ Amiram Eldar, Feb 16 2026

Crossrefs

Cf. A000005 (sigma_0), A000203 (sigma_1), A001157 (sigma_2).

Sequence in context: A116083 A115506 A243552 * A180814 A290679 A290423

Adjacent sequences: A057849 A057850 A057851 * A057853 A057854 A057855

Keyword

nonn

Author

Robert G. Wilson v, Nov 10 2000

Extensions

a(26)-a(34) from Donovan Johnson, Jun 08 2011

a(35)-a(37) from Amiram Eldar, Feb 16 2026

Status

approved