|
|
A306202
|
|
Matula-Goebel numbers of rooted semi-identity trees.
|
|
17
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|