

A008365


Smallest prime factor is >= 13.


10



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
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OFFSET

1,2


COMMENTS

Also the 13rough numbers: positive integers that have no prime factors less than 13.  Michael B. Porter, Oct 10 2009
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 prough numbers.
Benedict W. J. Irwin, Generating Function.
Eric Weisstein's World of Mathematics, Rough Number.
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


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 !! (n1)
a008365_list = 1 : filter ((> 11) . a020639) [1..]
 Reinhard Zumkeller, Jan 06 2013


CROSSREFS

For krough 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.


STATUS

approved



