A322386 Numbers whose prime indices are not prime and already belong to the sequence.

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

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: A306235 A353441 A004616 * A309583 A327478 A062846

Adjacent sequences: A322383 A322384 A322385 * A322387 A322388 A322389

Keyword

nonn

Author

Gus Wiseman, Dec 05 2018

Status

approved