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A062837
Numbers k such that k, 2*k+1, 3*k+1 are all squarefree.
1
2, 3, 6, 7, 10, 11, 14, 15, 19, 23, 26, 30, 34, 35, 38, 39, 42, 43, 46, 47, 51, 55, 59, 66, 70, 71, 74, 78, 79, 82, 86, 91, 95, 102, 106, 107, 110, 111, 115, 118, 119, 123, 127, 131, 134, 138, 142, 143, 146, 151, 154, 155, 159, 167, 170, 174, 178, 179, 182, 186
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is (7/3) * Product_{p prime} (1 - 3/p^2) = (7/3) * A206256 = 0.292802955446... (Tsang, 1985). - Amiram Eldar, Feb 26 2024
LINKS
Kai-Man Tsang, The distribution of r-tuples of square-free numbers, Mathematika, Vol. 32, No. 2 (1985), pp. 265-275.
MATHEMATICA
Select[Range[200], AllTrue[{#, 2#+1, 3#+1}, SquareFreeQ]&] (* Harvey P. Dale, Oct 20 2014 *)
PROG
(PARI) j=[]; for(n=1, 200, if(issquarefree(n) && issquarefree(2*n+1) && issquarefree(3*n+1), j=concat(j, n))); j
CROSSREFS
Subsequence of A005117 and A117204.
Cf. A206256.
Sequence in context: A042964 A338064 A230375 * A190670 A226115 A359503
KEYWORD
nonn
AUTHOR
Jason Earls, Jul 21 2001
STATUS
approved