OFFSET
1,1
COMMENTS
Numbers m such that the antiharmonic mean of the divisors of m is an integer but the arithmetic mean of the divisors of m is not an integer.
Numbers m such that B(m) = A001157(m) / A000203(m) is an integer but A(m) = A000203(m) / A000005(m) is not an integer.
Corresponding values of B(m): 3, 7, 11, 21, 21, 35, 43, 61, 63, 85, 111, 77, 91, 129, 119, 147, 185, 171, 273, 183, ...
Corresponding values of A(m): 7/3, 13/3, 31/5, 31/3, 91/9, 31/2, 127/7, 121/5, 217/9, 91/3, 133/3, ...
MATHEMATICA
Select[Range[1620], !Divisible[(sigma = DivisorSigma[1, #]), DivisorSigma[0, #]] && Divisible[DivisorSigma[2, #], sigma] &] (* Amiram Eldar, Nov 17 2019 *)
PROG
(Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and IsIntegral(&+[d^2: d in Divisors(m)] / SumOfDivisors(m))]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 17 2019
STATUS
approved