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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

It is well-known that the product of 11 consecutive integers is divisible by 11!. Conjecture: 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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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 !! (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

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)