A326310 Arithmetic numbers (A003601) that are not RMS numbers (A140480).

3, 5, 6, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102

Offset: 1

Author

Jaroslav Krizek, Oct 18 2019

Keywords

• nonn

Comments

Numbers m such that the arithmetic mean of the divisors of m is an integer but the quadratic mean (the root mean square) of the divisors of m is not an integer.

Numbers m such that A(m) = A000203(m) / A000005(m) is an integer but Q(m) = sqrt(A001157(m) / A000005(m)) is not an integer.

Corresponding values of A(m): 2, 3, 3, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 12, 22, 14, 13, 18, ...

Corresponding values of Q(m): sqrt(5), sqrt(13), sqrt(25/2), sqrt(61), sqrt(85), sqrt(125/2), sqrt(65), sqrt(145), sqrt(181), ...

Complement of A327055 with respect to A003601.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf.: A000005, A000203, A001157, A003601, A140480, A327055.

Programs

Magma

[m: m in [1..10^6] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(&+[d^2: d in Divisors(m)] / NumberOfDivisors(m)))];

Mathematica

Select[Range[120],IntegerQ[Mean[Divisors[#]]]&&!IntegerQ[RootMeanSquare[ Divisors[ #]]]&] (* Harvey P. Dale, Mar 04 2023 *)