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1, 3, 5, 9, 15, 19, 25, 33, 40, 52, 62, 70, 84, 96, 108, 124, 142, 156, 174, 198, 210, 230, 252, 268, 299, 327, 347, 371, 401, 425, 455, 487, 507, 543, 579, 607, 645, 681, 709, 757, 799, 823, 865, 905, 947, 991, 1037, 1069, 1112, 1174, 1210, 1266, 1320, 1360, 1420
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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a(n) = Sum_{k=1..n} Sum_{d|k} A101455(k/d) * d = Sum_{k=1..n} A050469(k).
G.f.: (1/(1 - x)) * Sum_{k>=1} k * x^k/(1 + x^(2*k)).
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MATHEMATICA
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f[2, e_] := 2^e; f[p_, e_] := If[Mod[p, 4] == 1, (p^(e + 1) - 1)/(p - 1), (p^(e + 1) + (-1)^e)/(p + 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Accumulate @ Array[s, 50] (* Amiram Eldar, Dec 18 2021 *)
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PROG
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(PARI) a(n) = sum(k=1, n, sumdiv(k, d, kronecker(-4, k/d)*d));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1+x^(2*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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