|
|
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
|
|
|
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).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|