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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

Table of n, a(n) for n=1..58.

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

Cf. A000081, A001678, A004111, A007097, A061775, A276625, A279861, A290689, A290760, A290822, A291636, A318185, A318187.

Sequence in context: A088879 A316470 A290822 * A139363 A091065 A328596

Adjacent sequences: A318183 A318184 A318185 * A318187 A318188 A318189

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 20 2018

STATUS

approved

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Last modified February 5 11:52 EST 2023. Contains 360084 sequences. (Running on oeis4.)