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
Robert P. P. McKone, Table of n, a(n) for n = 1..9999
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