A134602 Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).

378, 455, 527, 918, 1265, 1615, 2047, 2145, 2175, 2345, 2665, 3713, 3835, 4207, 4305, 4633, 5000, 5117, 5382, 6061, 6678, 6887, 6965, 7055, 7267, 7327, 7497, 7685, 7791, 8470, 8785, 8918, 9641, 10205, 10545, 10647, 11137, 11543, 11713, 13482, 14079

Offset: 1

Author

Hieronymus Fischer, Nov 11 2007

Keywords

• nonn

Comments

Numbers included in A134600, but not in A134601. a(1)=378 is the minimal number with this property.

Also numbers included in A134603, but not in A134604.

Examples

			a(2)=455, since 455=5*7*13 and sqrt((5^2+7^2+13^2)/3)=sqrt(81)=9.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134604, A134608, A134611, A134617, A134619, A134621.

Programs

Mathematica

f[{a_,b_}]:=Table[a,b];Select[Range[2,14079],!PrimeQ[#]&&!PrimeQ[ RootMeanSquare[f/@FactorInteger[#]//Flatten] ]&&IntegerQ[ RootMeanSquare[f/@FactorInteger[#]//Flatten] ]&] (* James C. McMahon, Apr 08 2025 *)

Extensions

Definition clarified by Hieronymus Fischer, Apr 20 2013, Jun 01 2013