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 A000477 a(n) = Sum_{k=1..n-1} k^2*sigma(k)*sigma(n-k). (Formerly M4973 N2135) 2
 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 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. A000441, A000499. Sequence in context: A247264 A212093 A212241 * A041430 A156941 A205440 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

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