The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A308668 a(n) = Sum_{d|n} d^(n/d+n). 3
 1, 9, 82, 1089, 15626, 287010, 5764802, 135270401, 3487315843, 100244173394, 3138428376722, 107072686593858, 3937376385699290, 155601328490478978, 6568412173896940652, 295165920677390712833, 14063084452067724991010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..385 FORMULA L.g.f.: -log(Product_{k>=1} (1 - k*(k*x)^k)^(1/k)) = Sum_{k>=1} a(k)*x^k/k. G.f.: Sum_{k>=1} k^(k+1) * x^k/(1 - k^(k+1) * x^k). - Seiichi Manyama, Mar 17 2021 MATHEMATICA a[n_] := DivisorSum[n, #^(n/# + n) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *) PROG (PARI) a(n) = sumdiv(n, d, d^(n/d+n)); (PARI) my(N=20, x='x+O('x^N)); Vec(x*deriv(-log(prod(k=1, N, (1-k*(k*x)^k)^(1/k))))) (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k+1)*x^k/(1-k^(k+1)*x^k))) \\ Seiichi Manyama, Mar 17 2021 (Python) from sympy import divisors def A308668(n): return sum(d**(n//d+n) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 19 2022 CROSSREFS Diagonal of A308502. Cf. A152211, A294956, A308594. Sequence in context: A294956 A294645 A338663 * A308481 A041146 A320991 Adjacent sequences: A308665 A308666 A308667 * A308669 A308670 A308671 KEYWORD nonn AUTHOR Seiichi Manyama, Jun 16 2019 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 December 4 07:45 EST 2022. Contains 358544 sequences. (Running on oeis4.)