A153193 - OEIS

%I #14 Mar 16 2022 02:56:57

%S 4,13,22,22,40,40,31,52,67,40,67,67,40,121,121,40,67,67,67,202,121,40,

%T 94,157,67,94,157,67,121,121,49,148,121,121,337,112,40,121,283,94,121,

%U 121,67,337,202,40,121,202,112,202,202,67,94,283,283,283,121,40

%N a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.

%C 1/n - 1/(n+1) - 1/k = 1/c where c is an integer, k >= 1.

%e 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

%e   k=1: 2*1/(1-2) = -2,

%e   k=3: 2*3/(3-2) =  6,

%e   k=4: 2*4/(4-2) =  4, and

%e   k=6: 2*6/(6-2) =  3.

%Y Cf. A146564, A152492, A063647, A000005, A146566.

%K nonn

%O 1,1

%A _Ctibor O. Zizka_, Dec 20 2008

%E a(13)-a(58) from _Jon E. Schoenfield_, Mar 15 2022