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A290822 Transitive numbers: Matula-Goebel numbers of transitive rooted trees. 49
1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 30, 32, 36, 38, 42, 48, 54, 56, 60, 64, 72, 76, 78, 84, 90, 96, 98, 106, 108, 112, 114, 120, 126, 128, 138, 144, 150, 152, 156, 162, 168, 180, 192, 196, 210, 212, 216, 222, 224, 228, 234, 238, 240, 252, 256, 262, 266, 270 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A number x is transitive if whenever prime(y) divides x and prime(z) divides y, we have prime(z) divides x.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

The sequence of transitive rooted trees 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))

30 (o(o)((o)))

32 (ooooo)

36 (oo(o)(o))

38 (o(ooo))

42 (o(o)(oo))

48 (oooo(o))

54 (o(o)(o)(o))

56 (ooo(oo))

60 (oo(o)((o)))

64 (oooooo)

72 (ooo(o)(o))

76 (oo(ooo))

78 (o(o)(o(o)))

84 (oo(o)(oo))

90 (o(o)(o)((o)))

96 (ooooo(o))

98 (o(oo)(oo))

MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

subprimes[n_]:=If[n===1, {}, Union@@Cases[FactorInteger[n], {p_, _}:>FactorInteger[PrimePi[p]][[All, 1]]]];

Select[Range[nn], Divisible[#, Times@@subprimes[#]]&]

CROSSREFS

Cf. A007097, A276625, A279861, A290689, A290760.

Sequence in context: A217562 A088879 A316470 * A318186 A139363 A091065

Adjacent sequences:  A290819 A290820 A290821 * A290823 A290824 A290825

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 19 2017

STATUS

approved

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Last modified June 16 15:17 EDT 2019. Contains 324152 sequences. (Running on oeis4.)