A326713 Numbers m that are neither arithmetic (A003601) nor RMS numbers (A140480).

2, 4, 8, 9, 10, 12, 16, 18, 24, 25, 26, 28, 32, 34, 36, 40, 48, 50, 52, 58, 63, 64, 72, 74, 75, 76, 80, 81, 82, 84, 88, 90, 98, 100, 104, 106, 108, 112, 117, 120, 121, 122, 124, 128, 130, 136, 144, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178

Offset: 1

Author

Jaroslav Krizek, Oct 18 2019

Keywords

• nonn

Comments

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.

Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.

Corresponding values of A(m): 3/2, 7/3, 15/4, 13/3, 9/2, 14/3, 31/5, 13/2, 15/2, 31/3, 21/2, 28/3, 21/2, 27/2, 91/9, 45/4, ...

Corresponding values of Q(m): sqrt(5/2), sqrt(7), sqrt(85/4), sqrt(91/3), sqrt(65/2), sqrt(35), sqrt(341/5), sqrt(455/6), ...

Sequence deviates from A049642; number 2217231104 (the first RMS number that is not arithmetic) is a term of A049642 but is not a term of this sequence.

Crossrefs

Cf. A000005, A000203, A001157, A003601, A049642, A140480, A327055.

Programs

Magma

[m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(&+[d^2: d in Divisors(m)] / NumberOfDivisors(m)))];

Mathematica

Select[Range[178], !IntegerQ @ RootMeanSquare[Divisors[#]] && !Divisible[ DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Oct 20 2019 *)