A255580 - OEIS

%I #24 Mar 13 2015 05:28:47

%S 119,161,455,527,595,721,833,959,1045,1081,1127,1241,1265,1547,1615,

%T 1855,2023,2047,2145,2275,2345,2665,2737,2975,3185,3281,3367,3703,

%U 3713,3835,3995,4165,4207,4305,4633,4681,5047

%N Numbers n such that n is not a prime power (p^k with k>=1) and the root mean square (quadratic mean) of its prime divisors is an integer.

%C Subsequence of A144711.

%H Daniel Lignon, <a href="/A255580/b255580.txt">Table of n, a(n) for n = 1..1000</a>

%p filter:= proc(n)

%p local P,p;

%p P:= numtheory:-factorset(n);

%p nops(P) > 1 and issqr(add(p^2,p=P)/nops(P))

%p end proc:

%p select(filter, [$1..10000]); # _Robert Israel_, Feb 26 2015

%t Complement[Select[Range[2,5000],IntegerQ[RootMeanSquare[Select[Divisors[#],PrimeQ]]]&],Select[Range[2,5000],Length[FactorInteger[#]]==1&]] (* _Daniel Lignon_, Feb 26 2015 *)

%o (PARI) isok(n) = ((nbp=omega(n)) > 1) && (f=factor(n)) && (x = sum(k=1, nbp, f[k,1]^2)/nbp) && issquare(x) && (type(x) == "t_INT"); \\ _Michel Marcus_, Mar 03 2015

%Y Cf. A144711 (Root mean square of prime divisors of n is an integer).

%K nonn

%O 1,1

%A _Daniel Lignon_, Feb 26 2015