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A344815
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a(n) = Sum_{k=1..n} floor(n/k) * 4^(k-1).
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8
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1, 6, 23, 92, 349, 1394, 5491, 21944, 87497, 349902, 1398479, 5593892, 22371109, 89484074, 357919803, 1431678080, 5726645377, 22906581142, 91626057879, 366504227292, 1466015859181, 5864063418866, 23456249463283, 93824997852744, 375299974563657, 1501199898183502
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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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a(n) = Sum_{k=1..n} Sum_{d|k} 4^(d-1).
G.f.: (1/(1 - x)) * Sum_{k>=1} x^k/(1 - 4*x^k).
G.f.: (1/(1 - x)) * Sum_{k>=1} 4^(k-1) * x^k/(1 - x^k).
a(n) = (1/3) * Sum_{k=1..n} (4^floor(n/k) - 1). - Ridouane Oudra, Feb 16 2023
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MAPLE
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seq(add(4^(k-1)*floor(n/k), k=1..n), n=1..60); # Ridouane Oudra, Feb 16 2023
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MATHEMATICA
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a[n_] := Sum[4^(k - 1) * Quotient[n, k], {k, 1, n}]; Array[a, 30] (* Amiram Eldar, May 29 2021 *)
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PROG
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(PARI) a(n) = sum(k=1, n, n\k*4^(k-1));
(PARI) a(n) = sum(k=1, n, sumdiv(k, d, 4^(d-1)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-4*x^k))/(1-x))
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, 4^(k-1)*x^k/(1-x^k))/(1-x))
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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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