

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 (MatulaGoebel numbers of seriesreduced 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



