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A376740
Numbers that have at least one two-digit prime factor.
1
11, 13, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 102, 104, 106, 110, 111, 114, 115, 116, 117
OFFSET
1,1
COMMENTS
Subsequence of A068191, first differing at A068191(55) = 101 which is not a term here.
Numbers k such that gcd(k,10978895066407230594062391177770267) > 1. - Chai Wah Wu, Nov 18 2024 [The big number is A109819(10) - Alois P. Heinz, Nov 18 2024]
The asymptotic density of this sequence is A051953(A109819(10))/A109819(10) = 1329644281346285477858013527/2807455661493975149742813527 = 0.473611... . - Amiram Eldar, Nov 19 2024
FORMULA
a(n + A051953(A109819(10))) = a(n) + A109819(10). - Amiram Eldar, Nov 19 2024
EXAMPLE
201 = 3*67 is in this sequence because it has one two-digit prime factor.
202 = 2*101 is not, because neither of them is two-digit.
MAPLE
q:= convert(select(isprime, [seq(i, i=11 .. 99, 2)]), `*`):
filter:= n -> igcd(n, q) > 1:
select(filter, [$1..200]); # Robert Israel, Nov 18 2024
MATHEMATICA
A376740Q[n_] := AnyTrue[FactorInteger[n][[All, 1]], 7 < # < 101 &];
Select[Range[200], A376740Q] (* Paolo Xausa, Nov 18 2024 *)
PROG
(Python)
def ok(n): return any(n%p == 0 for p in [11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97])
print([k for k in range(1, 118) if ok(k)]) # Michael S. Branicky, Oct 15 2024
(PARI) is(k) = {forprime(p = 11, 97, if(!(k % p), return(1))); 0; } \\ Amiram Eldar, Nov 19 2024
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Kishin Ikemoto, Oct 03 2024
STATUS
approved