A247142 -id:A247142 - cp's OEIS frontend

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

35, 49, 55, 145, 215, 341, 545, 589, 1189, 1681, 1769, 2449, 2641, 3005, 3131, 3599, 4681, 6931, 7601, 9899, 10469, 11215, 15871, 17639, 19511, 21691, 23711, 28345, 28369, 35429, 36521, 36811, 39059, 44609, 57121, 68189, 68759, 75349, 79921, 84419, 85801

Offset: 1

Daniel Lignon, Nov 20 2014

nonn

Of course, for all prime numbers the mean square of proper divisors is an integer.

			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

Amiram Eldar, Table of n, a(n) for n = 1..5000 (terms 1..100 from Daniel Lignon)

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).

Select[Range[2, 120000], (IntegerQ[RootMeanSquare[Most[Divisors[#]]]] && Not[PrimeQ[#]]) &]

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

cp's OEIS Frontend

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

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