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A008365 13-rough numbers: positive integers that have no prime factors less than 13. 13
1, 13, 17, 19, 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, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, 233, 239, 241, 247, 251, 257, 263, 269 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For n > 1, the smallest prime factor of a(n) is >= 13.
Conjecture: Numbers n such that n^24 is congruent to {1,421,631,841} mod 2310. - Gary Detlefs, Dec 30 2011
This sequence is exactly the set of positive values of r such that ( Product_{k = 0..10} n + k*r )/11! is an integer for all n. - Peter Bala, Nov 14 2015
The asymptotic density of this sequence is 16/77. - Amiram Eldar, Sep 30 2020
LINKS
Benedict W. J. Irwin, Generating Function.
Eric Weisstein's World of Mathematics, Rough Number.
FORMULA
G.f: x*P(x)/(1 - x - x^480 + x^481) where P(x) is a polynomial of degree 480. - Benedict W. J. Irwin, Mar 18 2016
77*n/16 - 13 < a(n) < 77*n/16 + 8. - Charles R Greathouse IV, Mar 21 2023
a(n) = a(n-1) + a(n-480) - a(n-481). - Charles R Greathouse IV, Mar 21 2023
MAPLE
for i from 1 to 500 do if gcd(i, 2310) = 1 then print(i); fi; od;
MATHEMATICA
Select[ Range[ 300 ], GCD[ #1, 2310 ]==1& ]
PROG
(PARI) isA008365(n) = gcd(n, 2310)==1 \\ Michael B. Porter, Oct 10 2009
(Haskell)
a008365 n = a008365_list !! (n-1)
a008365_list = 1 : filter ((> 11) . a020639) [1..]
-- Reinhard Zumkeller, Jan 06 2013
CROSSREFS
For k-rough numbers with other values of k, see A000027, A005408, A007310, A007775, A008364, A008365, A008366, A166061, A166063.
Sequence in context: A075761 A046064 A322274 * A132077 A235154 A045921
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
New name following a comment of Michael B. Porter, Mar 21 2023
STATUS
approved

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Last modified February 26 11:39 EST 2024. Contains 370352 sequences. (Running on oeis4.)