OFFSET
1,1
COMMENTS
Numbers m such that neither the arithmetic mean of the divisors of m nor the geometric mean of the divisors of m is an integer.
Corresponding values of A(m): 3/2, 15/4, 9/2, 14/3, 13/2, 15/2, 21/2, 28/3, 21/2, 27/2, 45/4, 62/5, 31/2, 49/3, 45/2, ...
Corresponding values of G(m): sqrt(2), sqrt(8), sqrt(10), sqrt(12), sqrt(18), sqrt(24), sqrt(26), sqrt(28), sqrt(32), ...
MATHEMATICA
Select[Range[230], !IntegerQ@Sqrt[#] && !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Nov 01 2019 *)
PROG
(Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(m))]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 31 2019
STATUS
approved