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A123707
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a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1).
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5
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1, 0, 1, 3, 7, 14, 31, 60, 126, 248, 511, 1005, 2047, 4064, 8183, 16320, 32767, 65394, 131071, 261885, 524255, 1048064, 2097151, 4193220, 8388600, 16775168, 33554304, 67104765, 134217727, 268427002, 536870911, 1073725440, 2147483135
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OFFSET
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1,4
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COMMENTS
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Triangle A123706 is the matrix inverse of triangle A010766(n,k) = [n/k].
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} mu(k) * x^k * (1 - x^k) / (1 - 2*x^k). - Ilya Gutkovskiy, Feb 06 2020
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MATHEMATICA
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t[n_, k_] := If[Divisible[n, k], MoebiusMu[n/k], 0] - If[Divisible[n, k + 1], MoebiusMu[n/(k + 1)], 0]; Table[Sum[t[n, k]*2^(k - 1), {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Oct 26 2017 *)
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PROG
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(PARI) {a(n)=sum(k=1, n, (matrix(n, n, r, c, if(r>=c, floor(r/c)))^-1)[n, k]*2^(k-1))}
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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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