A283596 Numbers m that divide sigma(m + k) where k is some divisor of m.

1, 2, 3, 4, 9, 12, 14, 20, 24, 30, 42, 56, 60, 84, 90, 108, 112, 120, 135, 150, 160, 168, 180, 240, 248, 312, 336, 504, 546, 624, 720, 728, 744, 780, 840, 882, 896, 900, 910, 992, 1008, 1092, 1120, 1152, 1344, 1440, 1456, 1488, 1680

Offset

1,2

Links

Michel Marcus, Table of n, a(n) for n = 1..500

Example

1(k = 1); 2(1); 3(3); 4(2); 9(1); 12(2, 3, 12); 14(14); 20(4); 24(6); ...

Maple

filter:= n -> ormap(t -> numtheory:-sigma(n+t) mod n = 0, numtheory:-divisors(n)): # Robert Israel, Mar 14 2017

Mathematica

Select[Range@ 1680, Function[n, Total@ Boole@ Map[Function[k, Divisible[DivisorSigma[1, n + k], n]], Divisors@ n] > 0]] (* Michael De Vlieger, Mar 15 2017 *)
ndsQ[n_]:=AnyTrue[DivisorSigma[1, n+Divisors[n]], Mod[#, n]==0&]; Select[ Range[ 2000], ndsQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 11 2018 *)

Prog

(PARI) isok(n) = fordiv (n, d, if (! (sigma(n+d) % n), return (1))); \\ Michel Marcus, Mar 15 2017

Crossrefs

Cf. A000203. Includes A110817.

Sequence in context: A062410 A145772 A027866 * A281992 A100902 A283447

Adjacent sequences: A283593 A283594 A283595 * A283597 A283598 A283599

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 14 2017

Status

approved