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A140664
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a(n) = A014963(n)*mobius(n).
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4
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1, -2, -3, 0, -5, 1, -7, 0, 0, 1, -11, 0, -13, 1, 1, 0, -17, 0, -19, 0, 1, 1, -23, 0, 0, 1, 0, 0, -29, -1, -31, 0, 1, 1, 1, 0, -37, 1, 1, 0, -41, -1, -43, 0, 0, 1, -47, 0, 0, 0, 1, 0, -53, 0, 1, 0, 1, 1, -59, 0, -61, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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A140579 as an infinite lower triangular matrix * A008683 as a vector, where A008683 = the mu sequence and A140579 is a diagonalized matrix version of A014963. Given the A008683, the mu sequence (1, -1, -1, 0, -1, 1, -1, 0, 0, 1,...), replace (-1) with (-n). Other mu(n) remain the same.
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MAPLE
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end proc:
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MATHEMATICA
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Table[Exp[MangoldtLambda[n]]*MoebiusMu[n], {n, 1, 75}] (* G. C. Greubel, Feb 15 2019 *)
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PROG
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(PARI) {a(n) = if(n==1, 1, gcd(vector(n-1, k, binomial(n, k)))*moebius(n))};
(Sage)
def A140664(n): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*moebius(n)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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