A298536 - OEIS

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A298536

Matula-Goebel numbers of rooted trees such that every branch of the root has a different number of leaves.

1, 2, 3, 5, 7, 11, 13, 14, 17, 19, 21, 23, 26, 29, 31, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 122, 123, 127, 129, 131, 133

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

EXAMPLE

Sequence of trees begins:

1 o

2 (o)

3 ((o))

5 (((o)))

7 ((oo))

11 ((((o))))

13 ((o(o)))

14 (o(oo))

17 (((oo)))

19 ((ooo))

21 ((o)(oo))

23 (((o)(o)))

26 (o(o(o)))

29 ((o((o))))

31 (((((o)))))

34 (o((oo)))

35 (((o))(oo))

37 ((oo(o)))

38 (o(ooo))

39 ((o)(o(o)))

41 (((o(o))))

43 ((o(oo)))

46 (o((o)(o)))

47 (((o)((o))))

MATHEMATICA

nn=2000;

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

leafcount[n_]:=If[n===1, 1, With[{m=primeMS[n]}, If[Length[m]===1, leafcount[First[m]], Total[leafcount/@m]]]];

Select[Range[nn], UnsameQ@@leafcount/@primeMS[#]&]

CROSSREFS

Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290689, A290760, A291442, A298534, A298535.

Sequence in context: A095179 A074895 A371653 * A331784 A325162 A331635

Adjacent sequences: A298533 A298534 A298535 * A298537 A298538 A298539

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 20 2018

STATUS

approved