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A366388
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The number of edges minus the number of leafs in the rooted tree with Matula-Goebel number n.
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6
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0, 0, 1, 0, 2, 1, 1, 0, 2, 2, 3, 1, 2, 1, 3, 0, 2, 2, 1, 2, 2, 3, 3, 1, 4, 2, 3, 1, 3, 3, 4, 0, 4, 2, 3, 2, 2, 1, 3, 2, 3, 2, 2, 3, 4, 3, 4, 1, 2, 4, 3, 2, 1, 3, 5, 1, 2, 3, 3, 3, 3, 4, 3, 0, 4, 4, 2, 2, 4, 3, 3, 2, 3, 2, 5, 1, 4, 3, 4, 2, 4, 3, 4, 2, 4, 2, 4, 3, 2, 4, 3, 3, 5, 4, 3, 1, 5, 2, 5, 4, 3, 3, 4, 2, 4
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OFFSET
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1,5
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COMMENTS
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Number of iterations of A366385 needed to reach the nearest power of 2.
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LINKS
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FORMULA
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Totally additive with a(2) = 0, and for n > 1, a(prime(n)) = 1 + a(n).
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EXAMPLE
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MATHEMATICA
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Array[-1 + Length@ NestWhileList[PrimePi[#2]*#1/#2 & @@ {#, FactorInteger[#][[-1, 1]]} &, #, ! IntegerQ@ Log2[#] &] &, 105] (* Michael De Vlieger, Oct 23 2023 *)
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PROG
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(PARI) A366388(n) = if(n<=2, 0, if(isprime(n), 1+A366388(primepi(n)), my(f=factor(n)); (apply(A366388, f[, 1])~ * f[, 2])));
(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
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CROSSREFS
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Cf. A109129 (gives the exponent of the nearest power of 2 reached), A196050 (distance to the farthest power of 2, which is 1).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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