login
A247136
Numbers for which the root mean square of nontrivial divisors is an integer.
2
4, 9, 25, 49, 119, 121, 161, 169, 289, 343, 361, 369, 527, 529, 711, 721, 833, 841, 959, 961, 1081, 1127, 1241, 1369, 1681, 1695, 1767, 1849, 2047, 2209, 2809, 3281, 3335, 3481, 3553, 3713, 3721, 4207, 4489, 4633, 4681, 5041, 5047, 5215, 5329, 6241, 6713, 6887
OFFSET
1,1
COMMENTS
All the squares of prime numbers (A001248) have this property but there are other numbers (A247137): 119,161,343,369,527,711,721,833,959,1081...
LINKS
Daniel Lignon and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 316 terms from Lignon)
FORMULA
Trivially a(n) << n^2 log^2 n. - Charles R Greathouse IV, Nov 20 2014
EXAMPLE
119 is a term because the nontrivial divisors of 119 are [7,17] and sqrt((7^2+17^2)/2)= 13 : it's an integer.
MATHEMATICA
Select[Range[2, 100000], (Not[PrimeQ[#]] && IntegerQ[ RootMeanSquare[ Rest[ Most[ Divisors[#]]]]])&]
PROG
(PARI) integralRMS(v)=my(t=norml2(v)/#v); denominator(t)==1 && issquare(t)
is(n)=my(d=divisors(n)); #d>2 && integralRMS(d[2..#d-1]) \\ Charles R Greathouse IV, Nov 20 2014
CROSSREFS
Cf. A140480 (numbers for which the root mean square of all divisors is an integer), A247136 (numbers for which the root mean square of proper divisors is an integer) and A023886 (numbers for which the arithmetic mean of nontrivial divisors is an integer).
Sequence in context: A344701 A182988 A158144 * A158145 A372743 A082180
KEYWORD
nonn
AUTHOR
Daniel Lignon, Nov 20 2014
STATUS
approved