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A166063
23-rough numbers: positive integers that have no prime factors less than 23.
11
1, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499
OFFSET
1,2
COMMENTS
Or, positive integers relatively prime to 9699690 = 2*3*5*7*11*13*17*19.
First composite term is 529 = 23^2.
FORMULA
a(n) = k*n + O(1) where k = 323323/55296 = 5.8471.... In particular, k*n - 51 < a(n) < k*n + 45. - Charles R Greathouse IV, Sep 21 2018
A166061 SETMINUS A332798 - R. J. Mathar, Nov 05 2024
EXAMPLE
667 = 23 * 29 is in the sequence since the two prime factors, 23 and 29, are not less than 23.
MAPLE
A166063 := proc(n)
option remember;
local a;
if n =1 then
1;
else
for a from procname(n-1)+1 do
numtheory[factorset](a) ;
if min(op(%)) >= 23 then
return a;
end if;
end do:
end if;
end proc:
seq(A166063(n), n=1..80) ; # R. J. Mathar, Nov 05 2024
MATHEMATICA
Select[Range[500], FactorInteger[#][[1, 1]]>22&] (* Harvey P. Dale, Nov 22 2010 *)
PROG
(PARI) isA166063(n) = gcd(n, 9699690)==1 \\ Michael B. Porter, Oct 10 2009
CROSSREFS
Cf. A332797 (subsequence).
Sequence in context: A255220 A060703 A061753 * A231073 A049483 A112681
KEYWORD
easy,nonn,changed
AUTHOR
Michael B. Porter, Oct 05 2009
EXTENSIONS
Additional terms provided provided by Harvey P. Dale, Nov 22 2010
STATUS
approved