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A235121
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Irregular triangle read by rows: row n contains in increasing order the Matula numbers of the rooted trees that are isomorphic as trees to the rooted tree with Matula number n (n>=1).
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2
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1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 11, 9, 10, 11, 9, 10, 11, 12, 13, 14, 17, 12, 13, 14, 17, 12, 13, 14, 17, 15, 22, 31, 16, 19, 12, 13, 14, 17, 18, 23, 26, 41, 16, 19, 20, 21, 29, 34, 59, 20, 21, 29, 34, 59, 15, 22, 31, 18, 23, 26, 41, 24, 37, 38, 67, 25, 33, 62, 127
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OFFSET
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1,2
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COMMENTS
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Number of entries in row n is A235122(n).
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LINKS
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FORMULA
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In order to construct the set A of numbers corresponding to row n, we start with A = {n} and we keep adjoining to A the numbers (x/p)' p", where x is an element of A, p is a prime factor of x, r' denotes the r-th prime and r" denotes the order of the prime r (i.e. r = r"-th prime). We do this until A becomes closed under the described operation. The Maple program (due to Edwin Clark) is based on this construction.
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EXAMPLE
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Row 11 is 9,10,11. Indeed the rooted tree with Matula number 11 is the path tree P[5] = ABCDE rooted at A; if rooted at B or D, then the Matula number is 10 and if rooted at C, then the Matula number is 9.
The triangle starts:
1;
2;
3,4;
3,4;
5,6;
5,6;
7,8;
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MAPLE
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with(numtheory): f := proc (m) local x, p, S: S := NULL: x := factorset(m): for p in x do S := S, ithprime(m/p)*pi(p) end do: S end proc: M := proc (m) local A, B: A := {m}: do B := A: A := `union`(map(f, A), A): if B = A then return A end if end do end proc: for j to 20 do M(j) end do; # yields sequence in triangular form; from W. Edwin Clark
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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