

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)).


24



4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 119, 121, 125, 128, 161, 169, 243, 256, 289, 343, 351, 361, 378, 455, 512, 527, 529, 595, 625, 721, 729, 841, 845, 918, 959, 961, 1024, 1045, 1081, 1241, 1265, 1323, 1331, 1369, 1375, 1547, 1615, 1681, 1792, 1849, 1855
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

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


EXAMPLE

a(5) = 25, since 25=5*5 and sqrt((5^2+5^2)/2)=5;
a(23) = 378, since 378=2*3*3*3*7 and sqrt((2^2+3*3^2+7^2)/5)=sqrt(16)=4.


CROSSREFS

Cf. A001597, A025475, A134333, A134344, A134376.
Cf. A134601, A134605, A134608, A134611, A134617, A134619, A134621.
Sequence in context: A249125 A306531 A088949 * A134601 A227476 A319163
Adjacent sequences: A134597 A134598 A134599 * A134601 A134602 A134603


KEYWORD

nonn


AUTHOR

Hieronymus Fischer, Nov 11 2007


EXTENSIONS

Definition clarified and edited by Hieronymus Fischer, Apr 20 2013


STATUS

approved



