If I understand your question.........!!!.
I wrote a short computer code and it found 2 sequences of positive consecutive 4-digit integers whose product divides 2010^2 evenly, and both are 12 consecutive terms as follows:
n=1000;p=0;a=productfor(m, n, n+p, (m));if(a%4040100==0, goto loop, goto next);printp;loop:printn,", ",;next:p++;if(p<=12, goto2,0);p=0;n++;if(n<9999, goto2, 0)
(4478, 4479, 4480, 4481, 4482, 4483, 4484, 4485, 4486, 4487, 4488, 4489)=12 terms mod 2010^2 =0
(8967, 8968, 8969, 8970, 8971, 8972, 8973, 8974, 8975, 8976, 8977, 8978) Total = 12 terms mod 2010^2=0
