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A153193
a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.
1
4, 13, 22, 22, 40, 40, 31, 52, 67, 40, 67, 67, 40, 121, 121, 40, 67, 67, 67, 202, 121, 40, 94, 157, 67, 94, 157, 67, 121, 121, 49, 148, 121, 121, 337, 112, 40, 121, 283, 94, 121, 121, 67, 337, 202, 40, 121, 202, 112, 202, 202, 67, 94, 283, 283, 283, 121, 40
OFFSET
1,1
COMMENTS
1/n - 1/(n+1) - 1/k = 1/c where c is an integer, k >= 1.
LINKS
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