cp's OEIS Frontend

A134601 Composite numbers such that the square mean of their prime factors is a prime (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).

%I A134601 #14 Apr 08 2025 23:29:42
%S A134601 4,8,9,16,25,27,32,49,64,81,119,121,125,128,161,169,243,256,289,343,
%T A134601 351,361,512,529,595,625,721,729,841,845,959,961,1024,1045,1081,1241,
%U A134601 1323,1331,1369,1375,1547,1681,1792,1849,1855,2048,2187,2197,2209,2401
%N A134601 Composite numbers such that the square mean of their prime factors is a prime (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
%C A134601 All perfect prime powers (A025475) with power > 0 are included.
%C A134601 Originally, the definition started with "Nonprime numbers ..." and the first term was equal to 1. This is misleading, since 1 has no prime factors. - _Hieronymus Fischer_, Apr 20 2013
%H A134601 Hieronymus Fischer, <a href="/A134601/b134601.txt">Table of n, a(n) for n = 1..10000</a>
%e A134601 a(5) = 25, since 25=5*5 and sqrt((5^2+5^2)/2)=5;
%e A134601 a(13) = 119, since 119=7*17 and sqrt((7^2+17^2)/2)=sqrt(169)=13.
%t A134601 f[{a_,b_}]:=Table[a,b];Select[Range[2,2401],!PrimeQ[#]&&PrimeQ[ RootMeanSquare[f/@FactorInteger[#]//Flatten] ]&] (* _James C. McMahon_, Apr 08 2025 *)
%Y A134601 Cf. A001597, A025475, A134333, A134344, A134376.
%Y A134601 Cf. A134600, A134605, A134608, A134611, A134617, A134619, A134621.
%K A134601 nonn
%O A134601 1,1
%A A134601 _Hieronymus Fischer_, Nov 11 2007
%E A134601 Definition clarified and edited by _Hieronymus Fischer_, Apr 20 2013