A327056 RMS numbers (A140480) that are not arithmetic (A003601).

2217231104, 6221622528, 9644780288, 12127073024, 15377570560, 15520617728, 22426778880, 43551357696, 67513462016, 84107119360, 84889511168, 90906475264, 107642993920, 156987452160, 255086523648, 446676800768, 497209993984, 529918233856, 588749835520, 636345326848

Offset: 1

Author

Jaroslav Krizek, Oct 18 2019

Keywords

• nonn

Comments

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.

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.

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

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

Complement of A327055 with respect to A140480.

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..39 (terms < 10^13)

Crossrefs

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

Programs

Magma

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

Extensions

a(13)-a(20) from Giovanni Resta, Oct 29 2019