%I #10 Sep 08 2022 08:46:24

%S 2217231104,6221622528,9644780288,12127073024,15377570560,15520617728,

%T 22426778880,43551357696,67513462016,84107119360,84889511168,

%U 90906475264,107642993920,156987452160,255086523648,446676800768,497209993984,529918233856,588749835520,636345326848

%N RMS numbers (A140480) that are not arithmetic (A003601).

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

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

%C Corresponding values of Q(m): 247511537, 368213825, 763370125, 957355945, 1237557685, 1237557685, 957355945, 1841069125, ...

%C Corresponding values of A(m): 418652080/9, 433603940/9, 324455362/3, 1166788784/9, 575646610/3, 1674608320/9, 315348320/3, ...

%C Complement of A327055 with respect to A140480.

%C Up to 10^13 there is only one odd term, a(29) = 3486482785825. Note that among the 7430 RMS numbers below 10^13 only 83 are even. - _Giovanni Resta_, Oct 29 2019

%H Giovanni Resta, <a href="/A327056/b327056.txt">Table of n, a(n) for n = 1..39</a> (terms < 10^13)

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

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

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 18 2019

%E a(13)-a(20) from _Giovanni Resta_, Oct 29 2019