OFFSET
1,1
COMMENTS
Given positive integers k, d with d | k+1, then n = k*(k+d+1+(k+1)/d) is a term, with the given k and j = k+d. - Robert Israel, Apr 22 2021
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
Let n = 24. Then (k+1)*(n/k +1), when k is taken over the divisors of 24, has the values: 50, 39, 36, 35, 35, 36, 39, 50. And (j+1)*((n+1)/j +1), when j is taken over the divisors of 25, has the values: 52, 36, 52.
Since 36 occurs in both lists of products, 24 is in sequence A143057.
MAPLE
filter:= proc(n) local k, a, j, r, q, d;
for k in numtheory:-divisors(n) do
a:= (k+1)*(n/k+1);
r:= (a-n)^2-4*a;
if issqr(r) then
q:= sqrt(r)/2;
for d in [a/2-n/2-1+q, a/2-n/2-1-q] do
if d::posint and n+1 mod d = 0 then return true fi
od
fi
od;
false
end proc:
select(filter, [$1..10000]); # Robert Israel, Apr 22 2021
MATHEMATICA
okQ[n_] := Module[{k, j}, k = Divisors[n]; j = Divisors[n+1]; Intersection[(k+1)(n/k+1), (j+1)((n+1)/j+1)] != {}];
Select[Range[2000], okQ] (* Jean-François Alcover, May 16 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Jul 20 2008
EXTENSIONS
Extended by R. J. Mathar, Aug 14 2008
STATUS
approved