cp's OEIS Frontend

A255580 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.

%I A255580 #24 Mar 13 2015 05:28:47
%S A255580 119,161,455,527,595,721,833,959,1045,1081,1127,1241,1265,1547,1615,
%T A255580 1855,2023,2047,2145,2275,2345,2665,2737,2975,3185,3281,3367,3703,
%U A255580 3713,3835,3995,4165,4207,4305,4633,4681,5047
%N A255580 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 A255580 Subsequence of A144711.
%H A255580 Daniel Lignon, <a href="/A255580/b255580.txt">Table of n, a(n) for n = 1..1000</a>
%p A255580 filter:= proc(n)
%p A255580 local P,p;
%p A255580 P:= numtheory:-factorset(n);
%p A255580 nops(P) > 1 and issqr(add(p^2,p=P)/nops(P))
%p A255580 end proc:
%p A255580 select(filter, [$1..10000]); # _Robert Israel_, Feb 26 2015
%t A255580 Complement[Select[Range[2,5000],IntegerQ[RootMeanSquare[Select[Divisors[#],PrimeQ]]]&],Select[Range[2,5000],Length[FactorInteger[#]]==1&]] (* _Daniel Lignon_, Feb 26 2015 *)
%o A255580 (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 A255580 Cf. A144711 (Root mean square of prime divisors of n is an integer).
%K A255580 nonn
%O A255580 1,1
%A A255580 _Daniel Lignon_, Feb 26 2015