|
| |
|
|
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
|
| |
|
|
