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A272349 Least multiple of n whose sum of divisors is divisible by n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 27 16:00 EDT 2022. Contains 354896 sequences. (Running on oeis4.)