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Numbers for which the root mean square of nontrivial divisors is an integer and which are not a square of prime numbers.
2

%I #18 Dec 10 2016 19:36:43

%S 119,161,343,369,527,711,721,833,959,1081,1127,1241,1695,1767,2047,

%T 3281,3335,3553,3713,4207,4633,4681,5047,5215,6713,6887,7327,7775,

%U 9641,12319,14031,16617,16999,18473,19199,22145,27009,27913,29449,31679,32239,32599,37241,44801,45385,47865,47959,50279,52319,56033

%N Numbers for which the root mean square of nontrivial divisors is an integer and which are not a square of prime numbers.

%C That's the numbers which are in A247136 and not in A001248.

%H Daniel Lignon and Charles R Greathouse IV, <a href="/A247137/b247137.txt">Table of n, a(n) for n = 1..10000</a> (terms up to 148 from Lignon)

%o (PARI) integralRMS(v)=my(t=norml2(v)/#v); denominator(t)==1 && issquare(t)

%o is(n)=my(d=divisors(n)); #d>3 && integralRMS(d[2..#d-1]) \\ _Charles R Greathouse IV_, Nov 20 2014

%Y Cf. A247136 (Numbers for which the root mean square of nontrivial divisors is an integer).

%K nonn

%O 1,1

%A _Daniel Lignon_, Nov 20 2014