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

1,2

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

Links

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

Formula

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

Example

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.

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

Prog

(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

Crossrefs

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

Sequence in context: A160729 A315801 A352135 * A262850 A262849 A115014

Adjacent sequences: A272346 A272347 A272348 * A272350 A272351 A272352

Keyword

nonn

Author

Waldemar Puszkarz, Apr 26 2016

Status

approved