OFFSET
1,2
COMMENTS
This sequence is the complement of A104210.
Equivalently, this sequence corresponds to the positive numbers k such that:
- A300820(k) <= 1,
For any n > 0 and k >= 0, a(n)^k belongs to the sequence.
The numbers of terms not exceeding 10^k, for k=1,2,..., are 9, 78, 758, 7544, 75368, 753586, 7535728, 75356719, 753566574, ... Apparently, the asymptotic density of this sequence is 0.75356... - Amiram Eldar, Apr 10 2021
Numbers not divisible by any term of A006094. - Antti Karttunen, Jul 29 2022
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
A300820(a(n)) <= 1.
EXAMPLE
The number 10 is only divisible by 2 and 5, hence 10 appears in the sequence.
The number 42 is divisible by 2 and 3, hence 42 does not appear in the sequence.
MAPLE
N:= 1000: # for terms <= N
R:= {}:
p:= 2:
do
q:= p; p:= nextprime(p);
if p*q > N then break fi;
R:= R union {seq(i, i=p*q..N, p*q)}
od:
sort(convert({$1..N} minus R, list)); # Robert Israel, Apr 13 2020
MATHEMATICA
q[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 == NextPrime[p1]] == 0; Select[Range[100], q] (* Amiram Eldar, Apr 10 2021 *)
PROG
(PARI) is(n) = my (f=factor(n)); for (i=1, #f~-1, if (nextprime(f[i, 1]+1)==f[i+1, 1], return (0))); return (1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Sep 25 2018
STATUS
approved