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A000441 a(n) = Sum_{k=1..n-1} k*sigma(k)*sigma(n-k).
(Formerly M4613 N1968)
9
0, 1, 9, 34, 95, 210, 406, 740, 1161, 1920, 2695, 4116, 5369, 7868, 9690, 13640, 16116, 22419, 25365, 34160, 38640, 50622, 55154, 73320, 77225, 100100, 107730, 135576, 141085, 182340, 184760, 233616, 243408, 297738, 301420, 385110, 377511, 467210, 478842 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Apart from initial zero this is the convolution of A340793 and A143128. - Omar E. Pol, Feb 16 2021
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39.
LINKS
J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy]
FORMULA
Convolution of A000203 with A064987. - Sean A. Irvine, Nov 14 2010
G.f.: x*f(x)*f'(x), where f(x) = Sum_{k>=1} k*x^k/(1 - x^k). - Ilya Gutkovskiy, Apr 28 2018
a(n) = (n/24 - n^2/4)*sigma_1(n) + (5*n/24)*sigma_3(n). - Ridouane Oudra, Sep 17 2020
Sum_{k=1..n} a(k) ~ Pi^4 * n^5 / 2160. - Vaclav Kotesovec, May 09 2022
MAPLE
S:=(n, e)->add(k^e*sigma(k)*sigma(n-k), k=1..n-1);
f:=e->[seq(S(n, e), n=1..30)]; f(1); # N. J. A. Sloane, Jul 03 2015
MATHEMATICA
a[n_] := Sum[k*DivisorSigma[1, k]*DivisorSigma[1, n-k], {k, 1, n-1}]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016 *)
PROG
(PARI) a(n) = sum(k=1, n-1, k*sigma(k)*sigma(n-k)); \\ Michel Marcus, Feb 02 2014
CROSSREFS
Cf. A000203 (sigma_1), A001158 (sigma_3), A064987.
Sequence in context: A326278 A014816 A147691 * A067989 A002881 A268803
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
a(1)=0 prepended by Michel Marcus, Feb 02 2014
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)