cp's OEIS Frontend

A265310 Least positive k such that the product of divisors of n (A007955) divides k!.

%I A265310 #18 Jan 06 2016 16:18:54
%S A265310 1,2,3,4,5,6,7,8,9,10,11,9,13,14,10,12,17,15,19,15,14,22,23,16,15,26,
%T A265310 15,21,29,20,31,16,22,34,14,21,37,38,26,20,41,28,43,33,15,46,47,24,21,
%U A265310 25,34,39,53,27,22,28,38,58,59,25,61,62,21,24,26,44,67,51,46,28,71,27,73
%N A265310 Least positive k such that the product of divisors of n (A007955) divides k!.
%C A265310 Conjecture: a(n) = n if and only if n is prime, 2*prime, 1, 8 or 9.
%H A265310 Robert Israel, <a href="/A265310/b265310.txt">Table of n, a(n) for n = 1..10000</a>
%p A265310 A265310:= proc(n) local F,f,tau,a,p,k;
%p A265310       F:= ifactors(n)[2];
%p A265310       tau:= mul(1+f[2],f=F);
%p A265310       k:= 1;
%p A265310       for f in F do
%p A265310         a:= f[2]*tau/2;
%p A265310         p:= f[1];
%p A265310         while add(floor(k/p^j),j=1..ilog[p](k)) < a do k:= p*(1+floor(k/p)) od;
%p A265310       od;
%p A265310       k
%p A265310 end proc:
%p A265310 map(A265310, [$1..100]); # _Robert Israel_, Dec 07 2015
%t A265310 Table[k = 1; While[! Divisible[k!, Times @@ Divisors@ n], k++]; k, {n, 73}] (* _Michael De Vlieger_, Dec 06 2015 *)
%o A265310 (PARI) a007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2));
%o A265310 a(n) = {k=1; while(k, if(k! % a007955(n)==0, return(k)); k++)}
%o A265310 vector(100, n, a(n)) \\ _Altug Alkan_, Dec 06 2015
%Y A265310 Cf. A007955.
%K A265310 nonn
%O A265310 1,2
%A A265310 _Gionata Neri_, Dec 06 2015