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A283596 Numbers n such that n divides sigma(n + k) where k is some divisor of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 21 02:48 EDT 2019. Contains 323434 sequences. (Running on oeis4.)