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%I #20 Sep 08 2022 08:46:24
%S 2,4,8,9,10,12,16,18,24,25,26,28,32,34,36,40,48,50,52,58,63,64,72,74,
%T 75,76,80,81,82,84,88,90,98,100,104,106,108,112,117,120,121,122,124,
%U 128,130,136,144,146,148,152,156,160,162,170,171,172,175,176,178
%N Numbers m that are neither arithmetic (A003601) nor RMS numbers (A140480).
%C Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.
%C Numbers m such that neither A(m) = A000203(m) / A000005(m) nor Q(m) = sqrt(A001157(m) / A000005(m)) is an integer.
%C 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, ...
%C 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), ...
%C 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.
%t Select[Range[178], !IntegerQ @ RootMeanSquare[Divisors[#]] && !Divisible[ DivisorSigma[1, #], DivisorSigma[0, #]] &] (* _Amiram Eldar_, Oct 20 2019 *)
%o (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)))]
%Y Cf. A000005, A000203, A001157, A003601, A049642, A140480, A327055.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, Oct 18 2019
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