The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A328203

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A328203

Expansion of Sum_{k>=1} k * x^k / (1 - x^(2*k))^2.
(history; published version)

#30 by Charles R Greathouse IV at Thu Sep 08 08:46:24 EDT 2022

PROG

(MAGMAMagma) a:=[]; for k in [1..65] do if IsOdd(k) then a[k]:=(k * #Divisors(k) + DivisorSigma(1, k)) / 2; else a[k]:=(k * (#Divisors(k) - #Divisors(k div 2)) + DivisorSigma(1, k) - DivisorSigma(1, k div 2)) / 2; end if; end for; a; // Marius A. Burtea, Oct 07 2019

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#29 by Peter Luschny at Thu Nov 18 12:45:10 EST 2021

STATUS

reviewed

approved

#28 by Michel Marcus at Thu Nov 18 11:24:19 EST 2021

STATUS

proposed

reviewed

#27 by Antti Karttunen at Thu Nov 18 09:55:14 EST 2021

STATUS

editing

proposed

Discussion

Thu Nov 18

10:03

Jon Maiga: This is probably the first time it would be helpful - at the same time I don't mind moving slowly either :)

#26 by Antti Karttunen at Thu Nov 18 09:55:00 EST 2021

FORMULA

The following two convolutions were found by Jon Maiga's SequenceDB Sequence Machine search algorithm. Both are easy to prove:

STATUS

proposed

editing

#25 by Antti Karttunen at Thu Nov 18 09:54:24 EST 2021

STATUS

editing

proposed

#24 by Antti Karttunen at Thu Nov 18 09:52:56 EST 2021

CROSSREFS

Cf. A000005, A000079 (fixed points), A000203, A001227, A002131, A003602, A006519, A006918, A026741, A038040, A109168, A113415, A140472, A152211, A193356, A245579, A349353 (Dirichlet inverse), A349354.

STATUS

proposed

editing

Discussion

Thu Nov 18

09:54

Antti Karttunen: Jon, I think you need a larger quota.

#23 by Jon Maiga at Thu Nov 18 09:28:32 EST 2021

STATUS

editing

proposed

#22 by Jon Maiga at Thu Nov 18 09:25:38 EST 2021

LINKS

Jon Maiga, <a href="http://sequencedb.net/s/A328203">Entry Computer-generated formulas for A328203</a>, Sequence DatabaseMachine.

STATUS

approved

editing

Discussion

Thu Nov 18

09:28

Jon Maiga: Name change, see A347957.

#21 by N. J. A. Sloane at Sun Nov 14 00:48:50 EST 2021

STATUS

proposed

approved