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 A247135 Composite numbers for which the root mean square of proper divisors is an integer. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)