OFFSET
1,2
COMMENTS
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 05 2018
STATUS
approved