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 A331489 Matula-Goebel numbers of topologically series-reduced rooted trees. 6
 1, 2, 7, 8, 16, 19, 28, 32, 43, 53, 56, 64, 76, 98, 107, 112, 128, 131, 152, 163, 172, 196, 212, 224, 227, 256, 263, 266, 304, 311, 343, 344, 383, 392, 424, 428, 443, 448, 512, 521, 524, 532, 577, 602, 608, 613, 652, 686, 688, 719, 722, 742, 751, 784, 848, 856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS We say that a rooted tree is topologically series-reduced if no vertex (including the root) has degree 2. The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of its branches. This gives a bijective correspondence between positive integers and unlabeled rooted trees. LINKS Eric Weisstein's World of Mathematics, Series-reduced tree. EXAMPLE The sequence of all topologically series-reduced rooted trees together with their Matula-Goebel numbers begins:     1: o     2: (o)     7: ((oo))     8: (ooo)    16: (oooo)    19: ((ooo))    28: (oo(oo))    32: (ooooo)    43: ((o(oo)))    53: ((oooo))    56: (ooo(oo))    64: (oooooo)    76: (oo(ooo))    98: (o(oo)(oo))   107: ((oo(oo)))   112: (oooo(oo))   128: (ooooooo)   131: ((ooooo))   152: (ooo(ooo))   163: ((o(ooo))) MATHEMATICA nn=1000; primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; srQ[n_]:=Or[n==1, With[{m=primeMS[n]}, And[Length[m]>1, And@@srQ/@m]]]; Select[Range[nn], PrimeOmega[#]!=2&&And@@srQ/@primeMS[#]&] CROSSREFS Unlabeled rooted trees are counted by A000081. Topologically series-reduced trees are counted by A000014. Topologically series-reduced rooted trees are counted by A001679. Labeled topologically series-reduced trees are counted by A005512. Labeled topologically series-reduced rooted trees are counted by A060313. Matula-Goebel numbers of lone-child-avoiding rooted trees are A291636. Cf. A000669, A001678, A007097, A007821, A060356, A061775, A109082, A109129, A196050, A254382, A276625, A330943, A331490. Sequence in context: A162664 A341706 A032689 * A300476 A213037 A287343 Adjacent sequences:  A331486 A331487 A331488 * A331490 A331491 A331492 KEYWORD nonn AUTHOR Gus Wiseman, Jan 20 2020 STATUS approved

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Last modified June 16 14:35 EDT 2021. Contains 345057 sequences. (Running on oeis4.)