The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000477 a(n) = Sum_{k=1..n-1} k^2*sigma(k)*sigma(n-k). (Formerly M4973 N2135) 8
 0, 1, 15, 76, 275, 720, 1666, 3440, 6129, 11250, 17545, 28896, 41405, 65072, 85950, 128960, 162996, 238545, 286995, 404600, 482160, 662112, 756470, 1042560, 1150625, 1549730, 1732590, 2257920, 2443105, 3250800, 3421160, 4452096, 4791600, 6039522, 6296500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 John Cerkan, Table of n, a(n) for n = 1..10000 J. Touchard, On prime numbers and perfect numbers, Scripta Math., 129 (1953), 35-39. [Annotated scanned copy] FORMULA a(n) = Sum_{k=1..n-1} k^2*sigma(k)*sigma(n-k). - Sean A. Irvine, Nov 14 2010 G.f.: x*f(x)*g'(x), where f(x) = Sum_{k>=1} k*x^k/(1 - x^k) and g(x) = Sum_{k>=1} k^2*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, May 02 2018 a(n) = (n^2/24 - n^3/6)*sigma_1(n) + (n^2/8)*sigma_3(n). - Ridouane Oudra, Sep 15 2020 Sum_{k=1..n} a(k) ~ Pi^4 * n^6 / 4320. - Vaclav Kotesovec, May 09 2022 EXAMPLE G.f. = x^2 + 15*x^3 + 76*x^4 + 275*x^5 + 720*x^6 + 1666*x^7 + 3440*x^8 + ... MAPLE with(numtheory): 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(2); # N. J. A. Sloane, Jul 03 2015 MATHEMATICA a[n_] := Sum[k^2 DivisorSigma[1, k] DivisorSigma[1, n-k], {k, 1, n-1}]; Array[a, 35] (* Jean-François Alcover, Feb 08 2016 *) PROG (PARI) a(n) = sum(k=1, n-1, k^2*sigma(k)*sigma(n-k)); \\ Michel Marcus, Feb 02 2014 CROSSREFS Cf. A000385, A000441, A000499, A259692, A259693, A259694, A259695, A259696. Cf. A000203 (sigma_1), A001158 (sigma_3). Sequence in context: A247264 A212093 A212241 * A302376 A041430 A156941 Adjacent sequences: A000474 A000475 A000476 * A000478 A000479 A000480 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 31 16:04 EDT 2023. Contains 361668 sequences. (Running on oeis4.)