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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 Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Peter Bala, A property of p-rough numbers. Benedict W. J. Irwin, Generating Function. Eric Weisstein's World of Mathematics, Rough Number. Index entries for linear recurrences with constant coefficients, order 481. Index entries for sequences related to smooth numbers 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 Adjacent sequences: A008362 A008363 A008364 * A008366 A008367 A008368 KEYWORD nonn,easy AUTHOR N. J. A. Sloane 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.)