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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 (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
Sequence in context: A217562 A088879 A316470 * A318186 A139363 A091065
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 19 2017
STATUS
approved

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Last modified February 23 15:29 EST 2024. Contains 370283 sequences. (Running on oeis4.)