A374840 a(n) is the greatest m > 0 such that the n-th row of Pascal's triangle (A007318) contains a multiple of k for k = 1..m.

1, 1, 2, 1, 4, 2, 6, 1, 2, 4, 10, 3, 12, 6, 4, 1, 16, 2, 18, 4, 6, 10, 22, 3, 4, 12, 2, 6, 28, 15, 30, 1, 10, 16, 6, 8, 36, 18, 12, 7, 40, 6, 42, 10, 8, 22, 46, 3, 6, 4, 16, 12, 52, 2, 10, 7, 18, 28, 58, 15, 60, 30, 8, 1, 12, 10, 66, 16, 22, 24, 70, 8, 72, 36

Offset

0,3

Comments

The sequence A006093 appears to give the fixed points of this sequence.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

For n = 6: the sixth row of Pascal's triangle is 1, 6, 15, 20, 15, 6, 1; it contains a multiple of 1 (1), of 2 (6), of 3 (6), of 4 (20), of 5 (15), of 6 (6), but not of 7, so a(6) = 6.

Maple

A374840 := proc(n)
    local dvsn , m, a;
    if n = 0 then
        return 1;
    end if;
    dvsn := {} ;
    for m from 1 to (n+2)/2 do
        binomial(n, m) ;
        dvsn := dvsn union numtheory[divisors](%) ;
    end do:
    for a from 1 do
        if not a in dvsn then
            return a-1 ;
        end if;
    end do:
end proc:
seq(A374840(n), n=0..40) ; # R. J. Mathar, Jul 30 2024
# second Maple program:
a:= proc(n) local k, s; s:= {seq(binomial(n, k), k=0..n/2)};
      for k while ormap(x-> irem(x, k)=0, s) do od: k-1
    end:
seq(a(n), n=0..73);  # Alois P. Heinz, Sep 04 2024

Mathematica

a[n_] := If[n == 0, 1, Module[{dd, m, k}, dd = {}; For[m = 1, m <= (n + 2)/2, m++, dd = Union[dd, Divisors[Binomial[n, m]]]]; For[k = 1, True, k++, If[FreeQ[dd, k], Return[k - 1]]]]];
Table[a[n], {n, 0, 73}] (* Jean-François Alcover, Sep 04 2024, after R. J. Mathar *)

Prog

(PARI) a(n) = { my (b = binomial(n)[1..(n+2)\2]); for (m = 2, oo, ok = 0; for (i = 1, #b, if (b[i] % m==0, next(2); ); ); return (m-1); ); }

Crossrefs

Cf. A006093, A007318, A249151.

Sequence in context: A173557 A023900 A141564 * A239641 A249151 A046791

Adjacent sequences: A374837 A374838 A374839 * A374841 A374842 A374843

Keyword

nonn

Author

Rémy Sigrist, Jul 22 2024

Status

approved