A350166 Partial sums of A050469.

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

Offset

1,2

Links

Winston de Greef, Table of n, a(n) for n = 1..10000

Formula

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)).

Mathematica

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 *)

Prog

(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))

Crossrefs

Cf. A050469, A101455, A350146.

Sequence in context: A018634 A310041 A029533 * A018685 A107994 A086748

Adjacent sequences: A350163 A350164 A350165 * A350167 A350168 A350169

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2021

Status

approved