A349546 Composite numbers k such that k+1 is divisible by (k+1 mod A001414(k)) and k-1 is divisible by (k-1 mod A001414(k)).

4, 8, 20, 32, 50, 55, 64, 77, 80, 98, 110, 115, 125, 128, 152, 170, 216, 242, 243, 256, 275, 290, 329, 338, 341, 343, 364, 371, 416, 506, 511, 512, 544, 551, 578, 583, 611, 638, 663, 722, 729, 731, 741, 851, 870, 920, 987, 1024, 1025, 1054, 1058, 1079, 1144, 1219, 1243, 1298, 1325, 1331, 1421

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 20 is a term because A001414(20) = 2+2+5 = 9, 20+1 = 21 is divisible by 21 mod 9 = 3, and 20-1 = 19 is divisible by 19 mod 9 = 1.

Maple

filter:= proc(n) local s, t, r, q;
  if isprime(n) then return false fi;
  s:= add(t[1]*t[2], t = ifactors(n)[2]);
  r:= (n+1) mod s;
  q:= (n-1) mod s;
  r<> 0 and q <> 0 and (n+1) mod r = 0 and (n-1) mod q = 0
end proc:
select(filter, [$4..2000]);

Mathematica

filter[n_] := Module[{s, t, r, q},
   If[ PrimeQ[n], Return[False]];
   s = Sum[t[[1]]*t[[2]], {t, FactorInteger[n]}];
   r = Mod[n+1, s];
   q = Mod[n-1, s];
   r != 0 && q != 0 && Mod[n+1, r] == 0 && Mod[n-1, q ] == 0];
Select[Range[4, 2000], filter] (* Jean-François Alcover, Sep 29 2024, after Maple program *)

Crossrefs

Cf. A001414.

Includes all members of A079704 except 18.

Sequence in context: A084922 A180794 A047185 * A034733 A365964 A152233

Adjacent sequences: A349543 A349544 A349545 * A349547 A349548 A349549

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 21 2021

Status

approved