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 A318186 Totally transitive numbers. Matula-Goebel numbers of totally transitive rooted trees. 7
 1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 32, 36, 38, 42, 48, 54, 56, 64, 72, 76, 78, 84, 96, 98, 106, 108, 112, 114, 126, 128, 144, 152, 156, 162, 168, 192, 196, 212, 216, 222, 224, 228, 234, 252, 256, 262, 266, 288, 294, 304, 312, 318, 324, 336, 342, 366, 378 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A number x is totally transitive if (1) whenever prime(y) divides x it follows that y is totally transitive and (2) if prime(y) divides x and prime(z) divides y then prime(z) also divides x. LINKS EXAMPLE The sequence of all totally transitive rooted trees together with their Matula-Goebel numbers 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)) 32: (ooooo) 36: (oo(o)(o)) 38: (o(ooo)) 42: (o(o)(oo)) 48: (oooo(o)) 54: (o(o)(o)(o)) 56: (ooo(oo)) 64: (oooooo) 72: (ooo(o)(o)) 76: (oo(ooo)) 78: (o(o)(o(o))) 84: (oo(o)(oo)) 96: (ooooo(o)) 98: (o(oo)(oo)) MATHEMATICA subprimes[n_]:=If[n==1, {}, Union@@Cases[FactorInteger[n], {p_, _}:>FactorInteger[PrimePi[p]][[All, 1]]]]; trmgQ[n_]:=Or[n==1, And[Divisible[n, Times@@subprimes[n]], And@@Cases[FactorInteger[n], {p_, _}:>trmgQ[PrimePi[p]]]]]; Select[Range[100], trmgQ] CROSSREFS Cf. A000081, A001678, A004111, A007097, A061775, A276625, A279861, A290689, A290760, A290822, A291636, A318185, A318187. Sequence in context: A088879 A316470 A290822 * A139363 A091065 A328596 Adjacent sequences: A318183 A318184 A318185 * A318187 A318188 A318189 KEYWORD nonn AUTHOR Gus Wiseman, Aug 20 2018 STATUS approved

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Last modified February 5 11:52 EST 2023. Contains 360084 sequences. (Running on oeis4.)