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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 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 Cf. A007097, A276625, A279861, A290689, A290760. Sequence in context: A217562 A088879 A316470 * A318186 A139363 A091065 Adjacent sequences: A290819 A290820 A290821 * A290823 A290824 A290825 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.)