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
Keywords
Links
- Daniel Lignon, Table of n, a(n) for n = 1..1000
Crossrefs
Cf. A144711 (Root mean square of prime divisors of n is an integer).
Programs
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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
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Mathematica
Complement[Select[Range[2,5000],IntegerQ[RootMeanSquare[Select[Divisors[#],PrimeQ]]]&],Select[Range[2,5000],Length[FactorInteger[#]]==1&]] (* Daniel Lignon, Feb 26 2015 *)
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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
Comments