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A069153
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a(n) = Sum_{d|n} d*(d-1)/2.
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12
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0, 1, 3, 7, 10, 19, 21, 35, 39, 56, 55, 91, 78, 113, 118, 155, 136, 208, 171, 252, 234, 287, 253, 395, 310, 404, 390, 497, 406, 614, 465, 651, 586, 698, 626, 910, 666, 875, 822, 1060, 820, 1202, 903, 1239, 1144, 1289, 1081, 1643, 1197, 1581, 1414, 1736
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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G.f. A(x) = (1/2) * x * d/dx log( B(x) ) where B() is g.f. for A052847. - Michael Somos, Feb 12 2008
G.f.: Sum_{k>0} ((k^2 - k) / 2) * x^k / (1 - x^k). - Michael Somos, Feb 12 2008
G.f.: A(x) = (1/2)* Sum_{n >= 1} x^(n^2)*( n*(n-1)*x^(3*n) - (n^2 + n - 2)*x^(2*n) + n*(3 - n)*x^n + n*(n - 1) )/(1 - x^n)^3. - differentiate equation 5 in Arndt twice w.r.t x and set x = 1. (End)
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EXAMPLE
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x^2 + 3*x^3 + 7*x^4 + 10*x^5 + 19*x^6 + 21*x^7 + 35*x^8 + 39*x^9 + 56*x^10 + ...
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MAPLE
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with(numtheory):
seq((1/2)*(sigma[2](n) - sigma[1](n)), n = 1..100); # Peter Bala, Jan 21 2021
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MATHEMATICA
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PROG
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(PARI) {a(n) = if( n<1, 0, sumdiv(n, d, d^2 - d) / 2)}
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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