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A322386 Numbers whose prime indices are not prime and already belong to the sequence. 2
1, 2, 4, 7, 8, 14, 16, 19, 28, 32, 38, 43, 49, 53, 56, 64, 76, 86, 98, 106, 107, 112, 128, 131, 133, 152, 163, 172, 196, 212, 214, 224, 227, 256, 262, 263, 266, 301, 304, 311, 326, 343, 344, 361, 371, 383, 392, 424, 428, 443, 448, 454, 512, 521, 524, 526, 532 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Union of A291636 (Matula-Goebel numbers of series-reduced rooted trees) and A322385.

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.

A multiplicative semigroup: if x and y are in the sequence, then so is x*y. - Robert Israel, Dec 06 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

1 has no prime indices, so the definition is satisfied vacuously. - Robert Israel, Dec 07 2018

We have 301 = prime(4) * prime(14). Since 4 and 14 already belong to the sequence, so does 301.

MAPLE

Res:= 1: S:= {1}:

for n from 2 to 1000 do

  F:= map(numtheory:-pi, numtheory:-factorset(n));

  if F subset S then

    Res:= Res, n;

    if not isprime(n) then S:= S union {n} fi

fi

od:

Res; # Robert Israel, Dec 06 2018

MATHEMATICA

tnpQ[n_]:=With[{m=PrimePi/@First/@If[n==1, {}, FactorInteger[n]]}, And[!MemberQ[m, _?PrimeQ], And@@tnpQ/@m]]

Select[Range[1000], tnpQ]

CROSSREFS

Cf. A000002, A001462, A007097, A079000, A079254, A214577, A276625, A291636, A304360, A320628, A322385.

Sequence in context: A336463 A306235 A004616 * A309583 A327478 A062846

Adjacent sequences:  A322383 A322384 A322385 * A322387 A322388 A322389

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 05 2018

STATUS

approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)