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A306202 Matula-Goebel numbers of rooted semi-identity trees. 12
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 70, 71, 73, 74, 76, 77, 78, 79, 80, 82, 84, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Definition: A positive integer belongs to the sequence iff its prime indices greater than 1 are distinct and already belong to the sequence. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

The sequence of all unlabeled rooted semi-identity trees together with their Matula-Goebel numbers begins:

   1: o

   2: (o)

   3: ((o))

   4: (oo)

   5: (((o)))

   6: (o(o))

   7: ((oo))

   8: (ooo)

  10: (o((o)))

  11: ((((o))))

  12: (oo(o))

  13: ((o(o)))

  14: (o(oo))

  15: ((o)((o)))

  16: (oooo)

  17: (((oo)))

  19: ((ooo))

  20: (oo((o)))

  21: ((o)(oo))

  22: (o(((o))))

  24: (ooo(o))

  26: (o(o(o)))

  28: (oo(oo))

  29: ((o((o))))

  30: (o(o)((o)))

MATHEMATICA

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

psidQ[n_]:=And[UnsameQ@@DeleteCases[primeMS[n], 1], And@@psidQ/@primeMS[n]];

Select[Range[100], psidQ]

CROSSREFS

Cf. A000081, A004111, A007097, A276625, A277098, A306200, A306201, A316467.

Sequence in context: A122132 A325389 A020662 * A328335 A302569 A235034

Adjacent sequences:  A306199 A306200 A306201 * A306203 A306204 A306205

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 29 2019

STATUS

approved

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Last modified May 31 22:11 EDT 2020. Contains 334756 sequences. (Running on oeis4.)