%I #72 Apr 19 2023 02:03:40

%S 1,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,169,173,179,181,

%U 191,193,197,199,211,221,223,227,229,233,239,241,247,251,257,263,269

%N 13-rough numbers: positive integers that have no prime factors less than 13.

%C For n > 1, the smallest prime factor of a(n) is >= 13.

%C Conjecture: Numbers n such that n^24 is congruent to {1,421,631,841} mod 2310. - _Gary Detlefs_, Dec 30 2011

%C 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

%C The asymptotic density of this sequence is 16/77. - _Amiram Eldar_, Sep 30 2020

%H Reinhard Zumkeller, <a href="/A008365/b008365.txt">Table of n, a(n) for n = 1..10000</a>

%H Peter Bala, <a href="/A008366/a008366_1.pdf">A property of p-rough numbers</a>.

%H Benedict W. J. Irwin, <a href="/A008365/a008365.txt">Generating Function</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RoughNumber.html">Rough Number</a>.

%H <a href="/index/Rec#order_481">Index entries for linear recurrences with constant coefficients</a>, order 481.

%H <a href="/index/Sk#smooth">Index entries for sequences related to smooth numbers</a>

%F 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

%F 77*n/16 - 13 < a(n) < 77*n/16 + 8. - _Charles R Greathouse IV_, Mar 21 2023

%F a(n) = a(n-1) + a(n-480) - a(n-481). - _Charles R Greathouse IV_, Mar 21 2023

%p for i from 1 to 500 do if gcd(i,2310) = 1 then print(i); fi; od;

%t Select[ Range[ 300 ], GCD[ #1, 2310 ]==1& ]

%o (PARI) isA008365(n) = gcd(n,2310)==1 \\ _Michael B. Porter_, Oct 10 2009

%o (Haskell)

%o a008365 n = a008365_list !! (n-1)

%o a008365_list = 1 : filter ((> 11) . a020639) [1..]

%o -- _Reinhard Zumkeller_, Jan 06 2013

%Y For k-rough numbers with other values of k, see A000027, A005408, A007310, A007775, A008364, A008365, A008366, A166061, A166063.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_

%E New name following a comment of _Michael B. Porter_, Mar 21 2023