login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069266 Numbers k such that Sum_{d|k} d/core(d) > 2*k, where core(d) is the squarefree part of d. 1
576, 1296, 2304, 3600, 5184, 7056, 8100, 9216, 11664, 14400, 17424, 20736, 24336, 28224, 32400, 36864, 44100, 46656, 57600, 63504, 69696, 72900, 82944, 90000, 97344, 104976, 108900, 112896, 129600, 147456, 152100, 156816, 166464, 176400, 186624, 202500, 207936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms <= 10^17 are squares. Are there any nonsquare terms? - David A. Corneth, Sep 05 2020

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5000 terms from Amiram Eldar)

FORMULA

Numbers k such that A068976(k) > 2*k.

EXAMPLE

3600 is in the sequence as its divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, ..., 400, 450, 600, 720, 900, 1200, 1800, 3600 and the respective values d/core(d) are 1, 1, 1, 4, 1, 1, 4, 9, ... , 900, 400, 900, 3600. The sum of this latter list is 7722 which is greater than 2*3600. - David A. Corneth, Sep 05 2020

MATHEMATICA

f[p_, e_] := If[OddQ[e], 2*(p^(e + 1) - 1)/(p^2 - 1), (p^(e + 2) + p^e - 2)/(p^2 - 1)]; Select[Range[2, 150000], Times @@ (f @@@ FactorInteger[#]) > 2*# &] (* Amiram Eldar, Sep 05 2020 *)

PROG

is(n) = sumdiv(n, d, d/core(d)) > n << 1 \\ David A. Corneth, Sep 05 2020

CROSSREFS

Cf. A068976, A007913.

Sequence in context: A109101 A258919 A064253 * A060678 A254848 A235181

Adjacent sequences:  A069263 A069264 A069265 * A069267 A069268 A069269

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, Apr 14 2002

EXTENSIONS

More terms from Amiram Eldar, Sep 05 2020

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)