

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.


2



119, 161, 455, 527, 595, 721, 833, 959, 1045, 1081, 1127, 1241, 1265, 1547, 1615, 1855, 2023, 2047, 2145, 2275, 2345, 2665, 2737, 2975, 3185, 3281, 3367, 3703, 3713, 3835, 3995, 4165, 4207, 4305, 4633, 4681, 5047
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OFFSET

1,1


COMMENTS

Subsequence of A144711.


LINKS

Daniel Lignon, Table of n, a(n) for n = 1..1000


MAPLE

filter:= proc(n)
local P, p;
P:= numtheory:factorset(n);
nops(P) > 1 and issqr(add(p^2, p=P)/nops(P))
end proc:
select(filter, [$1..10000]); # Robert Israel, Feb 26 2015


MATHEMATICA

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


PROG

(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


CROSSREFS

Cf. A144711 (Root mean square of prime divisors of n is an integer).
Sequence in context: A247137 A134603 A134604 * A227515 A207059 A257603
Adjacent sequences: A255577 A255578 A255579 * A255581 A255582 A255583


KEYWORD

nonn


AUTHOR

Daniel Lignon, Feb 26 2015


STATUS

approved



