OFFSET
1,2
COMMENTS
Also the 17-rough numbers: positive integers that have no prime factors less than 17. - Michael B. Porter, Oct 10 2009
a(n) - (1001/192) n is periodic with period 5760. - Robert Israel, Mar 18 2016
From Peter Bala, May 12 2018: (Start)
The product of two 17-rough numbers is a 17-rough number and the prime factors of a 17-rough number are 17-rough numbers.
Let k equal either 13, 14, 15 or 16. Then the product of k numbers n*(n + a)*(n + 2*a)*...*(n + (k-1)*a) in arithmetical progression is divisible by k! for all integer n if and only if a is a 17-rough number.
The sequence terms satisfy the congruence x^60 = 1 (mod 30030), where 30030 = 2*3*5*7*11*13. (End)
The asymptotic density of this sequence is 192/1001. - Amiram Eldar, Sep 30 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Peter Bala, A property of p-rough numbers.
Benedict Irwin, Generating Function.
Eric Weisstein's World of Mathematics, Rough Number.
FORMULA
Numbers n > 1 such that ((Sum_{k=1..n} k^10) mod n = 0) and ((Sum_{k=1..n} k^12) mod n = 0) (conjecture). - Gary Detlefs, Dec 27 2011
a(n) = a(n-1) + a(n-5760) - a(n-5761). - Vaclav Kotesovec, Mar 18 2016
G.f: x*P(x)/(1 - x - x^5760 + x^5761) where P(x) is a polynomial of degree 5760. - Benedict W. J. Irwin, Mar 23 2016
a(n) = (1001/192)*n + O(1), where the O(1) term is bounded by +/- 19. - Charles R Greathouse IV, Oct 13 2022
MAPLE
for i from 1 to 500 do if gcd(i, 30030) = 1 then print(i); fi; od;
MATHEMATICA
Select[ Range[ 300 ], GCD[ #1, 30030 ]==1& ]
Join[{1}, Select[Range[300], FactorInteger[#][[1, 1]]>=17&]] (* Harvey P. Dale, Mar 28 2020 *)
PROG
(PARI) isA008366(n) = gcd(n, 30030)==1 \\ Michael B. Porter, Oct 10 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved