cp's OEIS Frontend

A272349 Least multiple of n whose sum of divisors is divisible by n.

%I A272349 #29 May 02 2016 17:39:46
%S A272349 1,6,6,12,40,6,28,56,90,40,473,24,117,28,120,336,1139,90,703,120,420,
%T A272349 946,3151,120,3725,234,918,28,5017,120,496,672,891,2176,2660,792,2701,
%U A272349 1406,234,120,6683,420,11051,1892,270,6302,13207,528,2548,3800,3417,2340
%N A272349 Least multiple of n whose sum of divisors is divisible by n.
%C A272349 See A227470(n) for the sequence a(n)/n. If n = prime(i) is a prime then A097018 gives the answer: a(n) = n*A097018(i). One can show that a(n) always exists - see A227470 for the proof. - _N. J. A. Sloane_, May 01 2016
%H A272349 R. J. Mathar, <a href="/A272349/b272349.txt">Table of n, a(n) for n = 1..1000</a>
%F A272349 a(n) = n*A227470(n). - _R. J. Mathar_, May 02 2016
%e A272349 For n = 2, a(2) = 6 because it is the smallest number divisible by 2 whose sum of divisors (12) is also divisible by 2; 3 and 5 are not divisible by 2 and the sum of divisors of 2 and 4 is 3 and 7, hence also not divisible by 2.
%p A272349 A272349 := proc(n)
%p A272349     local k;
%p A272349     for k from 1 do
%p A272349         if modp(numtheory[sigma](k*n),n) =0 then
%p A272349             return k*n;
%p A272349         end if;
%p A272349     end do:
%p A272349 end proc: # _R. J. Mathar_, May 02 2016
%t A272349 A272349 = {}; Do[k = n; While[!(Divisible[k, n] && Divisible[DivisorSigma[1, k], n]), k++]; AppendTo[A272349, k], {n, 65}]; A272349
%o A272349 (PARI) for(n=1, 65, k=n; while(!(k%n==0&&sigma(k)%n==0), k++); print1(k ", "))
%o A272349 (PARI) a(n)=my(k=n); while(sigma(k)%n,k+=n); k \\ _Charles R Greathouse IV_, Apr 28 2016
%Y A272349 Cf. A000203, A097018 (if n is a prime), A227470.
%K A272349 nonn
%O A272349 1,2
%A A272349 _Waldemar Puszkarz_, Apr 26 2016