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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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).

Sequence in context: A034105 A034115 A212600 * A249819 A186319 A248659

Adjacent sequences: A247132 A247133 A247134 * A247136 A247137 A247138

Keyword

nonn

Author

Daniel Lignon, Nov 20 2014

Status

approved