|
|
A290822
|
|
Transitive numbers: Matula-Goebel numbers of transitive rooted trees.
|
|
58
|
|
|
1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 30, 32, 36, 38, 42, 48, 54, 56, 60, 64, 72, 76, 78, 84, 90, 96, 98, 106, 108, 112, 114, 120, 126, 128, 138, 144, 150, 152, 156, 162, 168, 180, 192, 196, 210, 212, 216, 222, 224, 228, 234, 238, 240, 252, 256, 262, 266, 270
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A number x is transitive if whenever prime(y) divides x and prime(z) divides y, we have prime(z) divides x.
|
|
LINKS
|
|
|
EXAMPLE
|
The sequence of transitive rooted trees begins:
1 o
2 (o)
4 (oo)
6 (o(o))
8 (ooo)
12 (oo(o))
14 (o(oo))
16 (oooo)
18 (o(o)(o))
24 (ooo(o))
28 (oo(oo))
30 (o(o)((o)))
32 (ooooo)
36 (oo(o)(o))
38 (o(ooo))
42 (o(o)(oo))
48 (oooo(o))
54 (o(o)(o)(o))
56 (ooo(oo))
60 (oo(o)((o)))
64 (oooooo)
72 (ooo(o)(o))
76 (oo(ooo))
78 (o(o)(o(o)))
84 (oo(o)(oo))
90 (o(o)(o)((o)))
96 (ooooo(o))
98 (o(oo)(oo))
|
|
MATHEMATICA
|
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
subprimes[n_]:=If[n===1, {}, Union@@Cases[FactorInteger[n], {p_, _}:>FactorInteger[PrimePi[p]][[All, 1]]]];
Select[Range[270], Divisible[#, Times@@subprimes[#]]&]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|