

A008366


Smallest prime factor is >= 17.


11



1, 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, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283
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OFFSET

1,2


COMMENTS

Also the 17rough 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 17rough numbers is a 17rough number and the prime factors of a 17rough number are 17rough numbers.
Let k equal either 13, 14, 15 or 16. Then the product of k numbers n*(n + a)*(n + 2*a)*...*(n + (k1)*a) in arithmetical progression is divisible by k! for all integer n if and only if a is a 17rough 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 prough numbers.
Benedict Irwin, Generating Function.
Eric Weisstein's World of Mathematics, Rough Number.
Index entries for sequences related to smooth numbers [Michael B. Porter, Oct 10 2009]


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(n1) + a(n5760)  a(n5761).  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


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

For krough numbers with other values of k, see A000027 A005408 A007310 A007775 A008364 A008365 A008366 A166061 A166063.  Michael B. Porter, Oct 10 2009
Cf. A005867.
Sequence in context: A054484 A054796 A322275 * A126769 A092216 A180948
Adjacent sequences: A008363 A008364 A008365 * A008367 A008368 A008369


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



