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A008365
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Smallest prime factor is >= 13.
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10
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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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history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Also the 13-rough 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
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LINKS
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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 sequences related to smooth numbers
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FORMULA
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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
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MAPLE
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for i from 1 to 500 do if gcd(i, 2310) = 1 then print(i); fi; od;
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MATHEMATICA
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Select[ Range[ 300 ], GCD[ #1, 2310 ]==1& ]
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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