cp's OEIS Frontend

A326310 Arithmetic numbers (A003601) that are not RMS numbers (A140480).

%I A326310 #26 Mar 16 2025 02:38:54
%S A326310 3,5,6,11,13,14,15,17,19,20,21,22,23,27,29,30,31,33,35,37,38,39,42,43,
%T A326310 44,45,46,47,49,51,53,54,55,56,57,59,60,61,62,65,66,67,68,69,70,71,73,
%U A326310 77,78,79,83,85,86,87,89,91,92,93,94,95,96,97,99,101,102
%N A326310 Arithmetic numbers (A003601) that are not RMS numbers (A140480).
%C A326310 Numbers m such that the arithmetic mean of the divisors of m is an integer but the quadratic mean (the root mean square) of the divisors of m is not an integer.
%C A326310 Numbers m such that A(m) = A000203(m) / A000005(m) is an integer but Q(m) = sqrt(A001157(m) / A000005(m)) is not an integer.
%C A326310 Corresponding values of A(m): 2, 3, 3, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 12, 22, 14, 13, 18, ...
%C A326310 Corresponding values of Q(m): sqrt(5), sqrt(13), sqrt(25/2), sqrt(61), sqrt(85), sqrt(125/2), sqrt(65), sqrt(145), sqrt(181), ...
%C A326310 Complement of A327055 with respect to A003601.
%H A326310 Giovanni Resta, <a href="/A326310/b326310.txt">Table of n, a(n) for n = 1..10000</a>
%t A326310 Select[Range[120],IntegerQ[Mean[Divisors[#]]]&&!IntegerQ[RootMeanSquare[ Divisors[ #]]]&] (* _Harvey P. Dale_, Mar 04 2023 *)
%o A326310 (Magma) [m: m in [1..10^6] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(&+[d^2: d in Divisors(m)] / NumberOfDivisors(m)))];
%Y A326310 Cf.: A000005, A000203, A001157, A003601, A140480, A327055.
%K A326310 nonn
%O A326310 1,1
%A A326310 _Jaroslav Krizek_, Oct 18 2019