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.

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

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