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A309322
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Expansion of Sum_{k>=1} phi(k) * x^k/(1 - x^k)^3, where phi = Euler totient function (A000010).
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5
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1, 4, 8, 15, 19, 35, 34, 56, 63, 86, 76, 141, 103, 157, 182, 212, 169, 294, 208, 355, 335, 359, 298, 556, 405, 490, 522, 657, 463, 865, 526, 816, 773, 812, 856, 1239, 739, 1003, 1058, 1424, 901, 1610, 988, 1525, 1617, 1445, 1174, 2188, 1435, 1960, 1760, 2091, 1483, 2529, 1994
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OFFSET
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1,2
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COMMENTS
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Dirichlet convolution of Euler totient function with triangular numbers.
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LINKS
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FORMULA
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a(n) = Sum_{d|n} phi(n/d) * d * (d + 1)/2.
a(n) = Sum_{k=1..n} Sum_{j=1..k} gcd(j,k,n).
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MATHEMATICA
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nmax = 55; CoefficientList[Series[Sum[EulerPhi[k] x^k/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[Sum[EulerPhi[n/d] d (d + 1)/2, {d, Divisors[n]}], {n, 1, 55}]
Table[Sum[Sum[GCD[j, k, n], {j, 1, k}], {k, 1, n}], {n, 1, 55}]
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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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