A328559 Numbers m that are neither arithmetic (A003601) nor squares (A000290).

2, 8, 10, 12, 18, 24, 26, 28, 32, 34, 40, 48, 50, 52, 58, 63, 72, 74, 75, 76, 80, 82, 84, 88, 90, 98, 104, 106, 108, 112, 117, 120, 122, 124, 128, 130, 136, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180, 192, 194, 200, 202, 208, 216, 218, 226

Offset: 1

Author

Jaroslav Krizek, Oct 31 2019

Keywords

• nonn

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.

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor G(m) = sqrt(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), ...

Crossrefs

Cf. A000005, A000203, A000290, A003601, A328557, A328558.

Programs

Magma

[m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(m))]

Mathematica

Select[Range[230], !IntegerQ@Sqrt[#] && !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Nov 01 2019 *)