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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
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
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 05 2018
STATUS
approved