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A316470 Matula-Goebel numbers of unlabeled rooted RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime. 22
1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 26, 28, 32, 36, 38, 42, 48, 52, 54, 56, 64, 72, 74, 76, 78, 84, 86, 96, 98, 104, 106, 108, 112, 114, 122, 126, 128, 144, 148, 152, 156, 162, 168, 172, 178, 182, 192, 196, 202, 208, 212, 214, 216, 222, 224, 228, 234, 244, 252 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff it is 1 or its prime indices are relatively prime and already belong to the sequence.
LINKS
EXAMPLE
The sequence of all RPMG-trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
4: (oo)
6: (o(o))
8: (ooo)
12: (oo(o))
14: (o(oo))
16: (oooo)
18: (o(o)(o))
24: (ooo(o))
26: (o(o(o)))
28: (oo(oo))
32: (ooooo)
36: (oo(o)(o))
38: (o(ooo))
42: (o(o)(oo))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Or[#==1, And[GCD@@primeMS[#]==1, And@@#0/@primeMS[#]]]&]
CROSSREFS
Sequence in context: A254748 A217562 A088879 * A290822 A318186 A139363
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved

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Last modified February 23 17:43 EST 2024. Contains 370283 sequences. (Running on oeis4.)