The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A046913

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A046913

Sum of divisors of n not congruent to 0 mod 3.
(history; published version)

#53 by R. J. Mathar at Wed May 17 04:04:39 EDT 2023

STATUS

editing

approved

#52 by R. J. Mathar at Wed May 17 04:04:24 EDT 2023

FORMULA

Equals A051731 * A091684, where A051731 = the inverse Mobius transform and A091684 = count with 3*n = 0: (1, 2, 0, 4, 5, 0, 7, ...). Example: a(4) = 7 = (1, 1, 0, 1) dot (1, 2, 0, 4) = (1 + 2 + 0 + 4), where (1, 1, 0, 1) = row 4 of A051731. - Gary W. Adamson, Jul 03 2008

Inverse Mobius transform of A091684. - Gary W. Adamson, Jul 03 2008

STATUS

approved

editing

#51 by Charles R Greathouse IV at Thu Sep 08 08:44:56 EDT 2022

PROG

(MAGMAMagma) [SumOfDivisors(3*k)-3*SumOfDivisors(k):k in [1..70]]; // Marius A. Burtea, Jun 01 2019

Discussion

Thu Sep 08

08:44

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

#50 by Bruno Berselli at Thu Sep 17 04:10:26 EDT 2020

STATUS

proposed

approved

#49 by Vaclav Kotesovec at Thu Sep 17 03:04:38 EDT 2020

STATUS

editing

proposed

#48 by Vaclav Kotesovec at Thu Sep 17 03:04:13 EDT 2020

FORMULA

Sum_{k=1..n} a(k) ~ Pi^2 * n^2 / 18. - Vaclav Kotesovec, Sep 17 2020

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proposed

editing

#47 by Amiram Eldar at Thu Sep 17 02:25:24 EDT 2020

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editing

proposed

#46 by Amiram Eldar at Thu Sep 17 02:15:12 EDT 2020

LINKS

H. Hershel M. Farkas, <a href="https://doi.org/10.1007/s11139-015004-97450141-15">On an arithmetical function</a>, Ramanujan J., Vol. 8(, No. 3) (2004), pp. 309-315.

Pavel Guerzhoy, and Ka Lun Wong, <a href="https://arxivdoi.org/abs/190510.065061007/s11139-020-00296-5">Farkas' identities with quartic characters</a>, The Ramanujan Journal (2020), <a href="https://arxiv.org/abs/1905.06506">preprint</a>, arXiv:1905.06506 [math.NT], 2019.

#45 by Amiram Eldar at Thu Sep 17 02:09:21 EDT 2020

MATHEMATICA

f[p_, e_] := If[p == 3, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *)

STATUS

approved

editing

#44 by Susanna Cuyler at Sat Jun 01 09:32:32 EDT 2019

STATUS

proposed

approved