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

1,1

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)

Prog

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

Crossrefs

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

Sequence in context: A288080 A274366 A224988 * A180688 A225760 A345722

Adjacent sequences: A327053 A327054 A327055 * A327057 A327058 A327059

Keyword

nonn

Author

Jaroslav Krizek, Oct 18 2019

Extensions

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

Status

approved