OFFSET
1,2
COMMENTS
The asymptotic density of this sequence is (3/2)*A065474 = 0.4839511484... (Granville and Ramaré, 1996). - Amiram Eldar, Feb 17 2021
REFERENCES
Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 184.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
Andrew Granville and Olivier Ramaré, Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients, Mathematika, Vol. 43, No. 1 (1996), pp. 73-107; alternative link.
FORMULA
Numbers k such that A000217(k) is squarefree. [corrected by Zak Seidov, Jun 05 2013]
EXAMPLE
14 is a term because A000217(14) = 14*15/2 = 105 = 3*5*7.
MATHEMATICA
Select[Range[123], SquareFreeQ[#(#+1)/2]&]
Position[Accumulate[Range[150]], _?(SquareFreeQ[#]&)]//Flatten//Rest (* Harvey P. Dale, Jul 07 2020 *)
PROG
(PARI) is(n)=issquarefree(n/gcd(n, 2))&&issquarefree((n+1)/gcd(n+1, 2)) \\ Charles R Greathouse IV, Jun 06 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Aug 22 2012
STATUS
approved