A217467 a(1) = 1; for n > 1, the maximum exponent k such that n^k divides the double factorial n!!.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 1, 2, 2, 1, 1, 5, 2, 1, 2, 2, 1, 3, 1, 6, 2, 1, 3, 4, 1, 1, 2, 4, 1, 3, 1, 2, 6, 1, 1, 10, 2, 3, 2, 2, 1, 4, 3, 4, 2, 1, 1, 7, 1, 1, 6, 10, 3, 3, 1, 2, 2, 5, 1, 8, 1, 1, 5, 2, 4, 3, 1, 9, 5, 1, 1, 6, 3, 1

Offset: 1

Author

Michel Lagneau, Oct 10 2012

Keywords

• nonn

Comments

n !! is a double factorial number (see the definition in A006882).

Examples

			24^5 = 7962624 divides 24!! = 1961990553600 but 24^6 does not so a(24)=5.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006882, A011776.

Programs

Maple

A217467 := proc(n)
    local df,k ;
    if n = 1 then
        return 1;
    end if;
    df := doublefactorial(n) ;
    for k from 1 do
        if (df mod n^(k+1)) <> 0 then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Oct 10 2012

Mathematica

Join[{1}, Table[IntegerExponent[n!!, n], {n, 2, 200}]]

PARI

a(n)={my(h=(n+1)\2); if (n==1, 1, valuation(if(n%2, (2*h)!/(2^h*h!), 2^h*h!), n))} \\ Andrew Howroyd, Feb 25 2018