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A118259
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Numbers of strongly carefree couples (a,b) with a,b <= n.
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3
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1, 3, 7, 7, 13, 17, 27, 27, 27, 33, 47, 47, 63, 73, 85, 85, 107, 107, 131, 131, 147, 165, 195, 195, 195, 215, 215, 215, 249, 265, 303, 303, 329, 355, 385, 385, 431, 461, 495, 495, 547, 569, 625, 625, 625, 661, 721, 721, 721, 721, 763, 763, 827, 827, 877, 877
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OFFSET
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1,2
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COMMENTS
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(a, b) is a strongly carefree couple if gcd(a, b) = 1 and both a and b are squarefree (A005117). - Amiram Eldar, Mar 03 2021
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree Couples, p. 110.
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LINKS
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FORMULA
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a(n) ~ A065473 * n^2 + O(n*log(n)). (End)
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MATHEMATICA
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Table[nn = n; Length[Select[Level[Table[Table[{i, j}, {i, 1, nn}], {j, 1, nn}], {2}], Apply[GCD, #] == 1 && SquareFreeQ[#[[1]]] &&SquareFreeQ[#[[2]]] &]], {n, 1, 56}] (* Geoffrey Critzer, Jan 13 2015 *)
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PROG
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(PARI) a(n)=sum(i=1, n, sum(j=1, n, moebius(i*j)^2)) \\ Benoit Cloitre, Oct 10 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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