cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A247135 Composite numbers for which the root mean square of proper divisors is an integer.

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%I A247135 #26 Oct 27 2019 11:11:42
%S A247135 35,49,55,145,215,341,545,589,1189,1681,1769,2449,2641,3005,3131,3599,
%T A247135 4681,6931,7601,9899,10469,11215,15871,17639,19511,21691,23711,28345,
%U A247135 28369,35429,36521,36811,39059,44609,57121,68189,68759,75349,79921,84419,85801
%N A247135 Composite numbers for which the root mean square of proper divisors is an integer.
%C A247135 Of course, for all prime numbers the mean square of proper divisors is an integer.
%H A247135 Amiram Eldar, <a href="/A247135/b247135.txt">Table of n, a(n) for n = 1..5000</a> (terms 1..100 from Daniel Lignon)
%e A247135 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 A247135 Select[Range[2, 120000], (IntegerQ[RootMeanSquare[Most[Divisors[#]]]] && Not[PrimeQ[#]]) &]
%o A247135 (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 A247135 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 A247135 nonn
%O A247135 1,1
%A A247135 _Daniel Lignon_, Nov 20 2014