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A306202 Matula-Goebel numbers of rooted semi-identity trees. 2
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 January 26 17:16 EST 2020. Contains 331280 sequences. (Running on oeis4.)