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A359733 a(n) = (1/2) * Sum_{d|n} (2*d)^(n/d). 1
1, 4, 7, 20, 21, 88, 71, 296, 373, 1084, 1035, 5084, 4109, 16496, 20787, 67728, 65553, 286516, 262163, 1070180, 1189937, 4194568, 4194327, 17760824, 16827241, 67109228, 72150655, 269503660, 268435485, 1104603808, 1073741855, 4303389216, 4476371181 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k>0} k * x^k / (1 - 2 * k* x^k).
MATHEMATICA
a[n_] := DivisorSum[n, (2*#)^(n/#) &] / 2; Array[a, 33] (* Amiram Eldar, Aug 14 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (2*d)^(n/d))/2;
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-2*k*x^k)))
CROSSREFS
Sequence in context: A275389 A127415 A045548 * A090879 A084404 A147065
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 12 2023
STATUS
approved

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Last modified June 12 20:44 EDT 2024. Contains 373360 sequences. (Running on oeis4.)