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A080267
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a(n) = Sum_{d divides n} d*2^(n-n/d).
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5
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1, 5, 13, 41, 81, 257, 449, 1313, 2497, 6465, 11265, 33665, 53249, 143617, 269313, 672257, 1114113, 3159041, 4980737, 13568001, 23904257, 57675777, 96468993, 275980289, 424673281, 1090535425, 1963720705, 4823482369, 7784628225
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k*2^(k-1)*x^k/(1 - 2^(k-1)*x^k). - N. J. A. Sloane, Jun 04 2003
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MAPLE
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oo := 40; s1 := add( k*2^(k-1)*x^k/(1-2^(k-1)*x^k), k=1..oo): s2 := series(s1, x, oo-1): s3 := seriestolist(%): A080267 := n->s3[n+1];
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MATHEMATICA
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PROG
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(PARI) a(n) = sumdiv(n, d, d*2^(n-n/d)); \\ Michel Marcus, Mar 20 2014
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(2*x)^k)^2)) \\ Seiichi Manyama, Dec 20 2022
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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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