OFFSET
1,1
COMMENTS
Numbers m such that the arithmetic mean of the divisors of m is an integer but the geometric mean of the divisors of m is not an integer.
Numbers m such that A(m) = A000203(m) / A000005(m) is an integer but G(m) = sqrt(m) is not an integer.
Corresponding values of A(m): 2, 3, 3, 4, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, ...
Corresponding values of G(m): sqrt(3), sqrt(5), sqrt(6), sqrt(7), sqrt(11), sqrt(13), sqrt(14), sqrt(15), sqrt(17), ...
MATHEMATICA
Select[Range[100], !IntegerQ @ Sqrt[#] && Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Oct 20 2019 *)
PROG
(Magma) [m: m in [1..10^5] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(m))]
(PARI) isA328557(n) = (!issquare(n)&&!(sigma(n)%numdiv(n))); \\ Antti Karttunen, Oct 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 19 2019
STATUS
approved