A134600 - OEIS

A134600

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

%I #10 Apr 21 2013 13:12:17

%S 4,8,9,16,25,27,32,49,64,81,119,121,125,128,161,169,243,256,289,343,

%T 351,361,378,455,512,527,529,595,625,721,729,841,845,918,959,961,1024,

%U 1045,1081,1241,1265,1323,1331,1369,1375,1547,1615,1681,1792,1849,1855

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

%C All perfect prime powers (A025475) with power > 0 are included.

%C 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 Hieronymus Fischer, <a href="/A134600/b134600.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 25, since 25=5*5 and sqrt((5^2+5^2)/2)=5;

%e a(23) = 378, since 378=2*3*3*3*7 and sqrt((2^2+3*3^2+7^2)/5)=sqrt(16)=4.

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

%Y Cf. A134601, A134605, A134608, A134611, A134617, A134619, A134621.

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Nov 11 2007

%E Definition clarified and edited by _Hieronymus Fischer_, Apr 20 2013