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

%I A217467 #26 Jan 14 2024 00:14:22
%S A217467 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,
%T A217467 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,
%U A217467 2,2,5,1,8,1,1,5,2,4,3,1,9,5,1,1,6,3,1
%N A217467 a(1) = 1; for n > 1, the maximum exponent k such that n^k divides the double factorial n!!.
%C A217467 n !! is a double factorial number (see the definition in A006882).
%H A217467 Andrew Howroyd, <a href="/A217467/b217467.txt">Table of n, a(n) for n = 1..10000</a>
%e A217467 24^5 = 7962624 divides 24!! = 1961990553600 but 24^6 does not so a(24)=5.
%p A217467 A217467 := proc(n)
%p A217467     local df,k ;
%p A217467     if n = 1 then
%p A217467         return 1;
%p A217467     end if;
%p A217467     df := doublefactorial(n) ;
%p A217467     for k from 1 do
%p A217467         if (df mod n^(k+1)) <> 0 then
%p A217467             return k;
%p A217467         end if;
%p A217467     end do:
%p A217467 end proc: # _R. J. Mathar_, Oct 10 2012
%t A217467 Join[{1}, Table[IntegerExponent[n!!, n], {n, 2, 200}]]
%o A217467 (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
%Y A217467 Cf. A006882, A011776.
%K A217467 nonn
%O A217467 1,8
%A A217467 _Michel Lagneau_, Oct 10 2012