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
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
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Apr 26 2016
STATUS
approved