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A291636 Matula-Goebel numbers of series-reduced rooted trees. 13
1, 4, 8, 14, 16, 28, 32, 38, 49, 56, 64, 76, 86, 98, 106, 112, 128, 133, 152, 172, 196, 212, 214, 224, 256, 262, 266, 301, 304, 326, 343, 344, 361, 371, 392, 424, 428, 448, 454, 512, 524, 526, 532, 602, 608, 622, 652, 686, 688, 722, 742, 749, 766, 784, 817 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An alternative definition: n is in the sequence iff n is 1 or the product of two or more not necessarily distinct prime numbers whose prime indices already belong to the sequence. For example, 14 is in the sequence because 14 = prime(1) * prime(4) and 1 and 4 both already belong to the sequence.

LINKS

Table of n, a(n) for n=1..55.

MATHEMATICA

nn=2000;

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

srQ[n_]:=Or[n===1, With[{m=primeMS[n]}, And[Length[m]>1, And@@srQ/@m]]];

Select[Range[nn], srQ]

CROSSREFS

Cf. A000081, A007097, A111299, A214577, A276625, A291441, A291442.

Sequence in context: A312335 A312336 A312337 * A320269 A036312 A312338

Adjacent sequences:  A291633 A291634 A291635 * A291637 A291638 A291639

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 28 2017

STATUS

approved

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Last modified July 23 22:36 EDT 2019. Contains 325270 sequences. (Running on oeis4.)