OFFSET
1,1
COMMENTS
1/n - 1/(n+1) - 1/k = 1/c where c is an integer, k >= 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The a(1)=4 integers of the form n*(n+1)*k/(k - n*(n+1)) = 1*(1+1)*k/(k - 1*(1+1)) = 2*k/(k-2) occur at
k=1: 2*1/(1-2) = -2,
k=3: 2*3/(3-2) = 6,
k=4: 2*4/(4-2) = 4, and
k=6: 2*6/(6-2) = 3.
MAPLE
f:= proc(n) local D;
D:= numtheory:-divisors((n*(n+1))^2);
nops(D) + nops(select(`<=`, D, n*(n+1)-1))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 21 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Ctibor O. Zizka, Dec 20 2008
EXTENSIONS
a(13)-a(58) from Jon E. Schoenfield, Mar 15 2022
STATUS
approved