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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

Table of n, a(n) for n=1..50.

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).floor())<m.mod(d):

................test=false

....return m

#insert blank line

n=50 #Change n for more terms

[FindM(k) for k in [1..n]] # Tom Edgar, Sep 03 2013

CROSSREFS

Sequence in context: A076079 A229593 A196007 * A276560 A049548 A005456

Adjacent sequences:  A134167 A134168 A134169 * A134171 A134172 A134173

KEYWORD

easy,nonn

AUTHOR

Bryce Herdt (mathidentity(AT)yahoo.com), Jan 12 2008

EXTENSIONS

More terms added and incorrect conjecture removed by Michel Marcus, Sep 03 2013

STATUS

approved

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Last modified November 18 12:16 EST 2019. Contains 329261 sequences. (Running on oeis4.)