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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
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
Gus Wiseman, Oct 19 2017
STATUS
approved