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 A292127 a(1) = 1, a(r(n)^k) = 1 + k * a(n) where r(n) is the n-th number that is not a perfect power A007916(n). 0
 1, 2, 3, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 7, 7, 8, 6, 7, 8, 8, 7, 9, 7, 7, 8, 9, 9, 6, 8, 10, 8, 7, 8, 9, 10, 10, 7, 9, 11, 9, 8, 9, 10, 11, 9, 11, 8, 10, 12, 10, 9, 10, 11, 12, 10, 12, 9, 11, 13, 7, 11, 10, 11, 12, 13, 11, 13, 10, 12, 14, 8, 12, 11 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Any positive integer greater than 1 can be written uniquely as a perfect power r(n)^k. We define a planted achiral (or generalized Bethe) tree b(n) for any positive integer greater than 1 by writing n as a perfect power r(d)^k and forming a tree with k branches all equal to b(d). Then a(n) is the number of nodes in b(n). LINKS EXAMPLE The first nineteen planted achiral trees are: o, (o), ((o)), (oo), (((o))), ((oo)), ((((o)))), (ooo), ((o)(o)), (((oo))), (((((o))))), ((ooo)), (((o)(o))), ((((oo)))), ((((((o)))))), (oooo), (((ooo))), ((((o)(o)))), (((((oo))))). MATHEMATICA nn=100; rads=Select[Range[2, nn], GCD@@FactorInteger[#][[All, 2]]===1&]; a[1]:=1; a[n_]:=With[{k=GCD@@FactorInteger[n][[All, 2]]}, 1+k*a[Position[rads, n^(1/k)][[1, 1]]]]; Array[a, nn] CROSSREFS Cf. A003238, A007916, A052409, A052410, A061775, A214577, A277576, A277615, A278028, A279614, A279944, A289023. Sequence in context: A061339 A073933 A056792 * A227861 A336751 A294991 Adjacent sequences:  A292124 A292125 A292126 * A292128 A292129 A292130 KEYWORD nonn AUTHOR Gus Wiseman, Sep 09 2017 STATUS approved

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)