The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Table of n, a(n) for n=1..33. 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 Cf. A055225, A076717. Sequence in context: A275389 A127415 A045548 * A090879 A084404 A147065 Adjacent sequences: A359730 A359731 A359732 * A359734 A359735 A359736 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Jan 12 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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