iBet uBet web content aggregator. Adding the entire web to your favor.

A008365

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

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

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.

Index entries for linear recurrences with constant coefficients, order 481.

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

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