A247137 -id:A247137 - cp's OEIS frontend

A247136 Numbers for which the root mean square of nontrivial divisors is an integer.

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

Daniel Lignon, Nov 20 2014

nonn

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...

			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.

Daniel Lignon and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 316 terms from Lignon)

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).

Select[Range[2,100000],(Not[PrimeQ[#]] && IntegerQ[ RootMeanSquare[ Rest[ Most[ Divisors[#]]]]])&]

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

Trivially a(n) << n^2 log^2 n. - Charles R Greathouse IV, Nov 20 2014

cp's OEIS Frontend

A247136 Numbers for which the root mean square of nontrivial divisors is an integer.

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