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%I #26 Oct 27 2019 11:11:42
%S 35,49,55,145,215,341,545,589,1189,1681,1769,2449,2641,3005,3131,3599,
%T 4681,6931,7601,9899,10469,11215,15871,17639,19511,21691,23711,28345,
%U 28369,35429,36521,36811,39059,44609,57121,68189,68759,75349,79921,84419,85801
%N Composite numbers for which the root mean square of proper divisors is an integer.
%C Of course, for all prime numbers the mean square of proper divisors is an integer.
%H Amiram Eldar, <a href="/A247135/b247135.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..100 from Daniel Lignon)
%e 35 is a term because it is not a prime, its proper divisors are {1, 5, 7} and sqrt((1^2 + 5^2 + 7^2)/3) = 5, an integer. - _Colin Barker_, Nov 20 2014
%t Select[Range[2, 120000], (IntegerQ[RootMeanSquare[Most[Divisors[#]]]] && Not[PrimeQ[#]]) &]
%o (PARI) s=[]; for(n=2, 120000, if(!isprime(n) && issquare((sigma(n, 2)-n^2)/(sigma(n, 0)-1)), s=concat(s, n))); s \\ _Colin Barker_, Nov 20 2014
%Y Cf. A247142 (numbers for which the root mean square of proper divisors is an integer), A140480 (numbers for which the root mean square of all divisors is an integer) and A023884 (numbers for which the arithmetic mean of proper divisors is an integer).
%K nonn
%O 1,1
%A _Daniel Lignon_, Nov 20 2014
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