OFFSET
1,1
COMMENTS
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..71
EXAMPLE
Divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; sum of sums of elements of subsets = 1 + 2 + 4 + 3 + 5 + 6 + 7 = 28 (perfect number).
sigma(16) * 2^(tau(16) - 1) = 31 * 16 = 496 (perfect number).
MAPLE
isA000396 := proc(n)
numtheory[sigma](n)=2*n ;
simplify(%) ;
end proc:
for n from 1 do
if isA000396(A229335(n)) then
print(n);
end if;
end do: # R. J. Mathar, Nov 10 2017
MATHEMATICA
Select[Range[2^20], DivisorSigma[1, DivisorSigma[1, #] 2^(DivisorSigma[0, #] - 1)] == 2 (DivisorSigma[1, #] 2^(DivisorSigma[0, #] - 1)) &] (* Michael De Vlieger, Nov 02 2017 *)
PROG
(Magma) [n: n in [1..10^6] | SumOfDivisors(SumOfDivisors(n)* (2^(NumberOfDivisors(n)-1))) eq 2*(SumOfDivisors(n)* (2^(NumberOfDivisors(n)-1)))];
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 02 2017
EXTENSIONS
Terms a(10) onward added by Max Alekseyev, Sep 18 2024
STATUS
approved