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.
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
New name following a comment of Michael B. Porter, Mar 21 2023
STATUS
approved