A272347 - OEIS

%I #20 Feb 15 2017 16:00:23

%S 1,2,9,8,40,12,56,8,9,40,88,12,104,56,60,80,136,18,152,40,84,88,184,

%T 24,225,104,108,56,232,60,248,96,132,136,560,36,296,152,156,40,328,84,

%U 344,88,180,184,376,96,441,450,204,104,424,108,880,56,228,232,472,60

%N Least number divisible by n and by the number of its own divisors.

%C By the sequence definition, all terms are refactorable numbers (A033950).

%C a(n) = n if and only if n is in A033950. - _Robert Israel_, Feb 15 2017

%H Robert Israel, <a href="/A272347/b272347.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=4, a(4)=8 because it is the smallest number divisible by 4 whose number of divisors (4) is also divisible by 4; 4 has 3 divisors and cannot be a term.

%p isA033950 := proc(n)

%p     if modp(n,numtheory[tau](n)) = 0 then

%p         true;

%p     else

%p         false;

%p     end if;

%p end proc:

%p A272347 := proc(n)

%p     local m;

%p     for m from 1 do

%p         if isA033950(m*n) then

%p             return m*n;

%p         end if;

%p     end do:

%p end proc:

%p seq(A272347(n),n=1..50) ; # _R. J. Mathar_, Apr 29 2016

%t f[n_] := Block[{m = n}, While[ Mod[m, DivisorSigma[0, m]] > 0, m += n];

%t m]; Array[f, 60] (* _Robert G. Wilson v_, Feb 15 2017 *)

%o (PARI) for(n=1, 75, k=n; while(!(k%n==0&&k%numdiv(k)==0), k++); print1(k ", "))

%Y Cf. A000005 (number of divisors), A033950 (refactorable numbers).

%K nonn,look

%O 1,2

%A _Waldemar Puszkarz_, Apr 26 2016