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Revision History for A013954

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A013954

a(n) = sigma_6(n), the sum of the 6th powers of the divisors of n.
(history; published version)

#40 by Michel Marcus at Sun Oct 29 02:34:34 EDT 2023

STATUS

reviewed

approved

#39 by Joerg Arndt at Sun Oct 29 02:10:29 EDT 2023

STATUS

proposed

reviewed

#38 by Amiram Eldar at Sun Oct 29 02:09:36 EDT 2023

STATUS

editing

proposed

#37 by Amiram Eldar at Sun Oct 29 01:44:16 EDT 2023

FORMULA

G.f.: sum_Sum_{k>=1} k^6*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

#36 by Amiram Eldar at Sun Oct 29 01:22:51 EDT 2023

DATA

1, 65, 730, 4161, 15626, 47450, 117650, 266305, 532171, 1015690, 1771562, 3037530, 4826810, 7647250, 11406980, 17043521, 24137570, 34591115, 47045882, 65019786, 85884500, 115151530, 148035890, 194402650, 244156251, 313742650, 387952660, 489541650, 594823322, 741453700

#35 by Amiram Eldar at Sun Oct 29 01:07:06 EDT 2023

LINKS

<a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

FORMULA

From Amiram Eldar, Oct 29 2023: (Start)

Multiplicative with a(p^e) = (p^(6*e+6)-1)/(p^6-1).

Dirichlet g.f.: zeta(s)*zeta(s-6).

Sum_{k=1..n} a(k) = zeta(7) * n^7 / 7 + O(n^8). (End)

CROSSREFS

Cf. A000203, A001014, A001157-A001160, A013665, A013955-A013972, A017665-A017712.

STATUS

approved

editing

#34 by Charles R Greathouse IV at Thu Sep 08 08:44:38 EDT 2022

PROG

(MAGMAMagma) [DivisorSigma(6, n): n in [1..30]]; // Bruno Berselli, Apr 10 2013

Discussion

Thu Sep 08

08:44

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

#33 by N. J. A. Sloane at Sat Dec 07 12:18:18 EST 2019

PROG

(Sage) [sigma(n, 6)for n in xrangerange(1, 24)] # Zerinvary Lajos, Jun 04 2009

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837

#32 by N. J. A. Sloane at Sat May 06 19:53:03 EDT 2017

STATUS

proposed

approved

#31 by Ilya Gutkovskiy at Sat May 06 17:58:37 EDT 2017

STATUS

editing

proposed