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

1,1

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A285785 A080759 A145714 * A047443 A173593 A268495

Adjacent sequences: A326307 A326308 A326309 * A326311 A326312 A326313

Keyword

nonn,changed

Author

Jaroslav Krizek, Oct 18 2019

Status

approved