login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134603 Numbers (excluding primes and powers of primes) such that the square mean of their prime factors is an integer (where the square mean of c and d is sqrt((c^2+d^2)/2)). 2
119, 161, 351, 378, 455, 527, 595, 721, 845, 918, 959, 1045, 1081, 1241, 1265, 1323, 1375, 1547, 1615, 1792, 1855, 2047, 2145, 2175, 2345, 2457, 2645, 2665, 2737, 3281, 3367, 3509, 3713, 3835, 3887, 3995, 4207, 4305, 4347, 4625, 4633, 4655, 4681, 5000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers included in A134600, but not in A025475. a(1)=119 is the minimal number with this property.

LINKS

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

EXAMPLE

a(2) = 161, since 161 = 7*23 and sqrt((7^2+23^2)/2) = sqrt(289) = 17 is an integer.

a(4) = 378, since 378 = 2*3*3*3*7 and sqrt((2^2+3*3^2+7^2)/5) = sqrt(80/5) = 4 is an integer.

a(28519) = 114445555, since 114445555 = 5*7*41*173*461 and sqrt((5^2+7^2+41^2+173^2+461^2)/5) = sqrt(48841) = 221.

CROSSREFS

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

Cf. A134600, A134605, A134608, A134611, A134617, A134619, A134621.

Sequence in context: A026049 A273179 A247137 * A134604 A255580 A227515

Adjacent sequences:  A134600 A134601 A134602 * A134604 A134605 A134606

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, Nov 11 2007

EXTENSIONS

Minor edits by the author, Apr 21 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 20:44 EST 2019. Contains 329849 sequences. (Running on oeis4.)