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

1, 6, 6, 12, 40, 6, 28, 56, 90, 40, 473, 24, 117, 28, 120, 336, 1139, 90, 703, 120, 420, 946, 3151, 120, 3725, 234, 918, 28, 5017, 120, 496, 672, 891, 2176, 2660, 792, 2701, 1406, 234, 120, 6683, 420, 11051, 1892, 270, 6302, 13207, 528, 2548, 3800, 3417, 2340

Offset: 1

Author

Waldemar Puszkarz, Apr 26 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A097018 (if n is a prime), A227470.

Programs

Maple

A272349 := proc(n)
    local k;
    for k from 1 do
        if modp(numtheory[sigma](k*n),n) =0 then
            return k*n;
        end if;
    end do:
end proc: # R. J. Mathar, May 02 2016

Mathematica

A272349 = {}; Do[k = n; While[!(Divisible[k, n] && Divisible[DivisorSigma[1, k], n]), k++]; AppendTo[A272349, k], {n, 65}]; A272349

PARI

for(n=1, 65, k=n; while(!(k%n==0&&sigma(k)%n==0), k++); print1(k ", "))

PARI

a(n)=my(k=n); while(sigma(k)%n,k+=n); k \\ Charles R Greathouse IV, Apr 28 2016

Formula

a(n) = n*A227470(n). - R. J. Mathar, May 02 2016