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a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*[(n+1) mod (k+1) = 0]*10^k, where [] denotes the Iverson bracket.
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%I #10 Oct 01 2018 03:30:02

%S 1,9,99,991,9999,100091,1000001,9999009,100000099,1000009991,

%T 10000000001,100000099109,1000000000001,9999999000009,100000000010099,

%U 999999990000991,9999999999999999,100000000100100091

%N a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*[(n+1) mod (k+1) = 0]*10^k, where [] denotes the Iverson bracket.

%o (PARI) tm(n) = hammingweight(n)%2;

%o a(n) = sum(k=0, n, if (((n+1) % (k+1))==0, (-1)^tm(n-k)*10^k)); \\ _Michel Marcus_, Oct 01 2018

%Y Cf. A010060, A101563, A051731.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Dec 07 2004