|
|
A375074
|
|
Numbers whose prime factorization exponents include at least one 2, at least one 3 and no higher exponents.
|
|
2
|
|
|
72, 108, 200, 360, 392, 500, 504, 540, 600, 675, 756, 792, 936, 968, 1125, 1176, 1188, 1224, 1323, 1350, 1352, 1368, 1372, 1400, 1404, 1500, 1656, 1800, 1836, 1960, 2052, 2088, 2200, 2232, 2250, 2312, 2484, 2520, 2600, 2646, 2664, 2700, 2888, 2904, 2952, 3087
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The asymptotic density of this sequence is 1/zeta(4) - 1/zeta(3) + 1/zeta(2) - zeta(6)/(zeta(2) * zeta(3)) * c = A215267 - A088453 + A059956 - A068468 * c = 0.0156712080080470088619..., where c = Product_{p prime} (1 + 2/p^3 - 1/p^4 + 1/p^5).
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
Select[Range[3000], Union[Select[FactorInteger[#][[;; , 2]], # > 1 &]] == {2, 3} &]
|
|
PROG
|
(PARI) is(k) = Set(select(x -> x > 1, factor(k)[, 2])) == [2, 3];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,new
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|