login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318186 Totally transitive numbers. Matula-Goebel numbers of totally transitive rooted trees. 7
1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 32, 36, 38, 42, 48, 54, 56, 64, 72, 76, 78, 84, 96, 98, 106, 108, 112, 114, 126, 128, 144, 152, 156, 162, 168, 192, 196, 212, 216, 222, 224, 228, 234, 252, 256, 262, 266, 288, 294, 304, 312, 318, 324, 336, 342, 366, 378 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A number x is totally transitive if (1) whenever prime(y) divides x it follows that y is totally transitive and (2) if prime(y) divides x and prime(z) divides y then prime(z) also divides x.
LINKS
EXAMPLE
The sequence of all totally transitive rooted trees together with 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))
28: (oo(oo))
32: (ooooo)
36: (oo(o)(o))
38: (o(ooo))
42: (o(o)(oo))
48: (oooo(o))
54: (o(o)(o)(o))
56: (ooo(oo))
64: (oooooo)
72: (ooo(o)(o))
76: (oo(ooo))
78: (o(o)(o(o)))
84: (oo(o)(oo))
96: (ooooo(o))
98: (o(oo)(oo))
MATHEMATICA
subprimes[n_]:=If[n==1, {}, Union@@Cases[FactorInteger[n], {p_, _}:>FactorInteger[PrimePi[p]][[All, 1]]]];
trmgQ[n_]:=Or[n==1, And[Divisible[n, Times@@subprimes[n]], And@@Cases[FactorInteger[n], {p_, _}:>trmgQ[PrimePi[p]]]]];
Select[Range[100], trmgQ]
CROSSREFS
Sequence in context: A088879 A316470 A290822 * A139363 A091065 A328596
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 20 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 21 22:50 EST 2024. Contains 370239 sequences. (Running on oeis4.)