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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 Vaclav Kotesovec, Table of n, a(n) for n = 1..1000 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. A000385, A000477, A000499, A259692, A259693, A259694, A259695, A259696. Cf. A000203 (sigma_1), A001158 (sigma_3), A064987. Cf. A143128, A340793. Sequence in context: A326278 A014816 A147691 * A067989 A002881 A268803 Adjacent sequences: A000438 A000439 A000440 * A000442 A000443 A000444 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 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)