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%I #10 May 09 2020 13:41:56
%S 1,1,2,3,2,2,3,4,3,3,3,4,3,3,4,5,3,5,3,4,4,4,3,6,3,5,5,5,2,4,6,6,3,3,
%T 5,8,4,3,4,7,2,5,5,6,5,3,4,8,5,6,4,5,4,6,4,6,5,5,3,8,2,5,7,8,4,5,4,6,
%U 4,5,5,9,4,5,6,6,3,5,5,9,7,4,3,8,5,4,5,6,4,8,6,5,5,4,5,9,3,6,7,10,4,5,4,6,5
%N a(n) = number of positive integers k where k divides (n - floor(n/k)).
%e For n = 8, checking: 1 divides (8 - floor(8/1))=0. 2 divides (8 - floor(8/2))=4. 3 divides (8 - floor(8/3))=6. 4 doesn't divide (8 - floor(8/4))=6. 5 doesn't divide (8 - floor(8/5))=7. 6 doesn't divide (8 - floor(8/6))=7. 7 divides (8 - floor(8/7))=7. 8 doesn't divide (8 - floor(8/8))=7. For k > 8, k doesn't divide (n - floor(n/k)) = n. There are 4 cases where k does divide (n-floor(n/k)); so a(8) = 4.
%t Join[{1},Table[Total[Table[If[Divisible[n-Floor[n/k],k],1,0],{k,n-1}]],{n,2,120}]] (* _Harvey P. Dale_, May 09 2020 *)
%K nonn
%O 1,3
%A _Leroy Quet_, Apr 26 2008
%E More terms from _R. J. Mathar_, Feb 27 2009
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