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

1,8

Comments

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

Links

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

Example

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

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}]]

Prog

(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

Crossrefs

Cf. A006882, A011776.

Sequence in context: A352823 A335234 A353854 * A268057 A107435 A196056

Adjacent sequences: A217464 A217465 A217466 * A217468 A217469 A217470

Keyword

nonn

Author

Michel Lagneau, Oct 10 2012

Status

approved