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 A134170 a(n) = the smallest positive integer which, expressed in the form d*q + r, satisfies q >= r for every d from 1 to n. In other words, when a(n) is divided by the numbers from 1 to n, the remainder is never more than the quotient. 1
 1, 2, 3, 4, 10, 12, 21, 24, 36, 40, 60, 60, 84, 84, 112, 112, 144, 144, 180, 180, 240, 252, 308, 336, 336, 400, 432, 432, 504, 540, 540, 651, 660, 660, 792, 792, 792, 936, 936, 936, 1080, 1092, 1092, 1260, 1260, 1260, 1440, 1440, 1440, 1680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If a prospective term is at least k(k-1) for a fixed value k, then the criterion will be satisfied for all d less than or equal to k. Note that a(n) >= n, otherwise quotient for n would be 0 and so condition on remainder would not be satisfied. - Michel Marcus, Sep 04 2013 LINKS EXAMPLE a(7)=21 because division by d=1 to 7 gives 21 r0, 10 r1, 7 r0, 5 r1, 4 r1, 3 r3 and 3 r0, respectively. MAPLE A134170 := proc(n)     local a, wrks, d;     for a from 1 do         wrks := true;         for d from 1 to n do             if modp(a, d) > floor(a/d) then                 wrks := false;                 break;             end if;         end do:         if wrks then             return a;         end if;     end do: end proc: # R. J. Mathar, Sep 04 2013 PROG (PARI) isok(m, n) = {for (d = 1, n, if (m\d < m%d, return (0)); ); return (1); } a(n) = {m = 1; while (! isok(m, n), m++); m; } \\ Michel Marcus, Sep 03 2013 (Sage) def FindM(n):     m=n-1     test=False     while not test:         test=True         m+=1         for d in [1..n]:             if Integer((m//d))

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)